Synchronized Express And Local Trains For Urban Commuter Rail Systems

ABSTRACT

A computerized system and method of managing subway trains along a two-track subway line to allow express travel in combination with local service. Express trains catch up to local trains at express stations along the line, and provision is made to allow the express trains to physically or “virtually” pass the local train at those stations. Embodiments in which the express trains physically pass the local train include direct train-to-train transfer facilitated by side-by-side tracks at the express station occupying reduced foot-print. In other embodiments, virtual passing is accomplished by changing the type of service provided by trains at express intervals: a local train “transforms” into an express train and vice versa. Embodiments enable passengers to transfer between trains at express stations so that these “relay” passengers can travel faster than any specific train.

BACKGROUND OF THE INVENTION

This invention is in the field of mass transit systems. Embodiments ofthis invention are more specifically directed to scheduling andoperation of mass transit commuter rail systems.

For many years, citizens of major metropolitan areas throughout theworld have relied on commuter rail systems, including surface rail andsubways, as an important means of transportation. Because at-gradeintersections with motor vehicles are avoided by subway trains, subwaysystems are especially attractive in densely populated cities.Currently, over one hundred cities in the world operate subway commuterrail systems, serving hundreds of millions of passengers each day.

Commuter rail systems in general, and subway systems in particular, areof course constrained to the physical locations of their tracks andstations. Trains cannot travel except along the rails, and do not stopfor loading and unloading except at discrete stations along the railway.The construction cost of the infrastructure components of railways,rails, and stations is a primary determination in the overall size andcomplexity of a subway system, especially considering the excavationrequired to build a subway line within (and thus under) an existingcity. Because of these constraints, and of the cost required to addlines or additional infrastructure, optimal utilization of thetransportation capacity provided by the subway commuter rail system is ahighly desirable goal. Underutilization of the subway system is afinancial disaster, in that the huge infrastructure costs are notrecouped; as such, subway commuter rail construction is often confinedto routes that are capable of providing adequate ridership. But theseinfrastructure costs also inhibit additional capacity from beingconstructed, if demand for the subway system exceeds its capacity. As aresult, many of the world's urban subway systems are overcrowded;indeed, the overcrowded subway systems in Seoul, Korea and Tokyo, Japanoften receive worldwide publicity. My U.S. Pat. No. 5,176,082, issuedJan. 5, 1993, describes a passenger loading and unloading control systemthat provides one way of addressing this overcrowding problem,specifically by scheduling the number of passengers that may boardindividual train cars at a station according to the number of passengersthat are already on those cars; a method of simultaneously loading andunloading passengers, in an orderly manner, is also described in mypatent.

The constraint of high infrastructure construction costs is alsoreflected in passenger travel times. Commuter rail systems present theparticular problem that passengers are free to board and exit the subwaytrain at any station along the line. For example, a train that makes nstops along its line will have Σ_(j=2) ^(n)(j−1) possible individualpassenger trips, with the particular trip made by a given passengerdefined by the station at which the passenger boards (i.e., the triporigin) and the station at which the passenger chooses to exit the train(i.e., the destination). And, of course, ridership depends on theconvenience provided by the subway, which in large part depends on theproximity of subway stations to passenger destinations. The subwaysystem designer and operator is thus faced with a tradeoff between thenumber of stations along a line and the passenger travel time fromorigin to terminus. Specifically, while a larger number of stationsalong a line improves the proximity of the subway to a wide range ofdestinations, this larger number of stations will necessarily slow thepassenger travel time of passengers that do not want to exit the trainat a particular station.

One conventional approach to solving the two problems of overcrowdedsubway train systems and long passenger travel times is the use ofexpress trains, which are trains that do not stop at every station alonga line. In some of the larger subway systems, such as those in New YorkCity, Paris, and Seoul, separate railways and station platforms areprovided for the express and local trains, enabling the express trainsto travel the route without being held up by the slower local trainsthat stop at each station. In these systems with separate express linesand stations, in which the express trains are not slowed by local trainsand stops at local stations, those passengers that board at an expressstation, remain on an express train throughout their trip, and exit atan express station, have the optimum passenger travel time.

However, many passengers must ride a local train either to travel to anexpress station, or to travel from the express station to their desireddestination, or both. If these passengers wish to take advantage of theexpress train service, they must make a transfer between the local andexpress lines at least once during their trip. The total travel time forthese passengers thus includes not only the travel time while on thetrains, but also the transfer time involved in changing trains at theexpress stations. One can consider this transfer time to be the sum ofseveral components, including the boarding and deboarding times, thetime required for the passenger to walk between the express and localplatforms (typically on different subway levels), and also the timespent waiting for the “transfer-to” train to arrive at the station.Typically, the wait time dominates this transfer time, and can beconsidered as a random variable, with a mean value of about ½ the“headway” time of the “transfer-to” train.

By way of further background, it is known to synchronize the arrival anddeparture times of express trains at express stations with the arrivaland departure times of local trains at those stations, during rush hourperiods of the day. For example, the New York City subway system hasbeen known to schedule their express subway service to minimize transfertimes between express and local trains, at least during morning rushhour periods. In this way, the wait time that passengers spend waitingfor the “transfer-to” train to arrive at the station is reduced.

As evident from this description, however, those subway systems orportions of subway systems that are limited to only a single track ineach direction of travel have not been able to provide express service.In such systems, the ultimate speed of travel of an express train, whichas such does not stop at local stations located between expressstations, will eventually necessarily be limited by the speed of anylocal train that the express train catches up to along the route.

By way of further background, “side tracks” or “sidings” are used insome railway systems to allow a faster train to pass a stopped or slowertrain. FIG. 1 a illustrates, in plan view, an example of a conventionalpassenger rail station at which faster trains are allowed to pass sloweror stopped trains, using side tracks. In this example, the two-tracksystem includes main line 2WE for trains traveling “west” to “east” inthe view of FIG. 1 a, and main line 2EW for trains traveling “east” to“west”. Main line 2WE is disposed adjacent to platform 5WE, at whichpassenger are able to board and de-board west-to-east traveling trains,while main line 2EW is disposed adjacent to platform 5EW, which supportspassenger boarding and deboarding for east-to-west travel. Thisconventional station includes side tracks 4WE, 4EW associated withplatforms 5WE, 5EW, respectively. Side tracks 4WE, 4EW can each becoupled to their respective main tracks 2WE, 2EW, such that a traintraveling along main track 2WE, for example, can switch over to andtravel along side track 4WE at this station, or can instead continue onmain track 2WE. As evident from FIG. 1 a, in this conventionalarrangement, a slower train approaching the station from the west onmain track 2WE can switch over to side track 4WE and stop at platform5WE, allowing a faster train such as an express train to remain on maintrack 2WE and travel past platform 5WE, effectively passing the slowertrain that is stopped at platform 5WE on side track 4WE. As such, atwo-track subway line including stations such as the conventionalstation shown in FIG. 1 a can support express and local service.

Side track facilities are typically more prevalent at surface railstations than at subway stations, because the excavation cost etc.involved in adding a side track at a subway station is typicallyprohibitive. For example, as shown in FIG. 1 a, the station must besufficiently wide (vertical dimension in FIG. 1) to include the two maintracks 2WE, 2EW, two platforms 5WE, 5EW, two side tracks 4WE, 4EW, andthe appropriate spacing on either side of each of these structures. Ifan existing two-track system wished to add express service, the cost ofadding side tracks 4WE, 4EW in the manner shown in FIG. 1 a isespecially prohibitive, and for that reason is seldom carried out. Andeven in those surface or subway systems in which side tracks areprovided at stations, significant wait time is often required forpassengers to change from one train to another, as mentioned above.

By way of further background, computer algorithms for optimizing thescheduling of trains are known in the art. U.S. Pat. No. 6,873,962 B1describes an automated approach for scheduling departure times andvelocities of trains traveling along a rail corridor, by deriving andoptimizing a cost function that ensures that all intersections (trainsmeeting or passing one another) occur at locations at which side tracksare in place. U.S. Patent Application Publication No. US 2005/0234757 A1describes an automated scheduling system for freight trains, in arailway system including side tracks to allow faster trains to passslower or stopped trains. U.S. Patent Application Publication No. US2005/0261946 A1 also describes a method and system for calculating atrain schedule plan that operates by optimizing a cost function tominimize delays at crossing loops and lateness at key locations alongtrain routes. U.S. Patent Application No. US 2008/0109124 A1 describes atrain scheduling method in which placeholders (“virtual consists”) areused to improve the stability of the solution.

However, each of these conventional train scheduling methods and systemsapply to the scheduling of trains that are not concerned with allowingpassengers to board or de-board at intermediate stations along theroute. In other words, these scheduling methods do not involve theproblem of passenger transfer from one train to another, nor do theyaccount for trains that allow for the payload to efficiently board andde-board at any particular stop along the route. In other words, theseconventional scheduling methods and systems do not solve many of theimportant and dominant issues involved in commuter rail systems,particularly subway systems.

By way of further background, U.S. Pat. No. 1,604,932 describes apassenger train system in which passenger throughput is increased byproviding trains that are longer than the available platforms. Some carsin the train stop at the platform of every station, while other cars inthe train stop at the platform only at alternating stations. The carsand platforms are color-coded, so that the passengers are aware of therestrictions.

By way of further background, it is well known in the urbantransportation field that customer demand varies greatly between peakhours of the day (e.g., morning and evening “rush hours” during workdays) and non-peak hours and days (e.g., weekends, holidays, and mid-dayand night hours of work days). For the case of a typical rush hourduration of 2½ hours, twice per work day, a given subway line operatesin a non-rush hour state for on the order of three-fourths of eachworkday. One study has shown that over 80% of the workday passengers ofsubway lines, worldwide, occur during rush hour periods. As such, onecan roughly determine that the passenger load per hour of a typical citysubway line can be more than twenty times greater in rush hour periodsthan in non-rush hour periods. As such, if the subway operator operatestrains identically during rush hour and non-rush hour periods, thepassenger loading of the trains during non-rush hour periods isextremely light; conversely, the train utilization during non-rush hourperiods is very low.

Many subway lines address this inefficiency in subway train usage byreducing the frequency of train service during non-rush hour periods.However, this approach is known to even further depress passenger demandduring non-rush hour periods, as some passengers will use availablealternative modes of transportation rather than endure inordinately longwaits at the station. Reduced frequency of service especially increasesthe travel time for those passengers who must make inter-line transfers.Another conventional approach for improving the efficiency of the subwaysystem in non-rush hour periods is to shorten the length of the trains,such that each train has fewer cars (and thus greater utilization ofseats) during non-rush hour periods than it would with full-lengthtrains. However, the number of operator personnel required in thisapproach is essentially the same as if the trains were of full length.In addition, additional personnel and operational complexity resultsfrom the tasks of coupling and decoupling cars from trains, parking thedecoupled cars, and the like. As such, considering that a large majorityof even the workday is outside of the rush hours, efficient utilizationof transportation infrastructure, rolling stock, and personnel has notbeen attained in conventional subway systems.

BRIEF SUMMARY OF THE INVENTION

It is therefore an object of this invention to provide a system andmethod of operating a subway train system that optimizes the utilizationof subway system resources including the subway tracks, subway stations,and subway trains, while substantially reducing passenger travel timefor all passengers.

It is a further object of this invention to provide synchronizedconnections between express and local trains, throughout the year, ateach express station in express/local urban commuter rail systems.

It is a further object of this invention to provide optimum connectionsbetween express and local trains at each express station, with minimumpassenger transfer time between the express and local trains.

It is a further object of this invention to reduce passenger totaltravel time at minimal system cost, resulting in reduced overcrowding ofsubway trains by improving the passenger throughput rate of the system.

It is a further object of this invention to provide such a system andmethod that is adapted to new or existing two-track subway systems.

It is a further object of this invention to provide such a system andmethod of that enables express trains to operate on the same subway lineas local trains, while enabling the express trains to reduce the traveltimes of the express passengers.

It is a further object of this invention to provide such a system andmethod in which passenger transfer times at express stations areminimized.

It is a further object of this invention to provide such a system andmethod in which express service is provided without requiring theconstruction of side tracks or other infrastructure at the expressstations.

It is a further object of this invention to provide such a system andmethod that facilitates the changing of trains at express stations toprovide passengers with the opportunity to further reduce their traveltime in exchange for minimal effort on their part, indeed to reducetheir travel time to such an extent that a passenger can travel alongthe route at an effective speed that is faster than the fastest subwaytrain travels along that route.

It is a further object of this invention to minimize the time spent byan arriving train waiting for a train at the station to leave thestation, while providing the additional convenience to passengers ofextra stops along the express route.

It is a further object of this invention to improve the utilization ofrolling stock and operating personnel during non-rush hour periods,without significantly impacting the frequency of service at stops alongthe route.

Other objects and advantages of this invention will be apparent to thoseof ordinary skill in the art having reference to the followingspecification together with its drawings.

According to one aspect of this invention, the departures and velocitiesof express and local subway trains are synchronized so that the expresstrain arrives at express stations at approximately the same time as thelocal service train that is ahead of the express train on the sametrack. A novel side track and transfer system is provided to allow theexpress train to pass the local train at the express station, and toallow passengers to transfer directly between the stopped local andexpress trains without deboarding to a platform and waiting at theplatform.

According to another aspect of this invention, the departures andvelocities of express and local subway trains are synchronized so thatthe express train arrives at express stations at approximately the sametime as the local service train that is ahead of the express train onthe same track. At the express station, one or more of the trainstransform from providing local service to providing express service, sothat the last of the trains to arrive at the express station at a giventime transforms from an express train to a local train, with the firstone of the trains arriving at that station at that time transforms froma local train to an express train. Each passenger remaining on one ofthe trains thus travels at express speeds for at least a portion of thetrip.

According to another aspect of this invention, the synchronized trainsarriving at an express station at approximately the same time areshuttled at the platform to allow passengers to transfer from a trainthat is transforming from express to local service, to a train that istransforming from local to express service. These passengers can thustravel at express speeds for all but the necessary local legs of theirtrip. Indeed, it is possible for these transferring passengers to arriveat their eventual destination after a travel time that is shorter thanthat of the fastest train along that route.

According to another aspect of this invention, the later-arriving of thesynchronized trains arriving at an express station is scheduled so thatit makes an additional stop along its express leg, thus minimizing timethat it must wait for the earlier-arriving synchronized train to leavethe express station while improving customer convenience.

According to another aspect of this invention, fewer stations along thesubway line are designated as express stations during non-rush hourperiods than during rush hour periods. In effect, the interval betweenexpress stations is scaled longer, for example by a multiple of two,three, or four. This scaling of the express station interval, and thusthe scaling of the “group train dispatching interval”, reduces thenumber of stations at which the express train passes a local train. Byincluding additional “semi-express” stations along the scaled expressstation interval, and because customer load is lighter during non-rushhour periods, fewer trains can provide the same frequency of service asduring rush hour periods.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 a is a schematic diagram, in plan view, of a conventional trainstation with side tracks.

FIGS. 1 b through 1 d are schematic diagrams, in plan view, of theoperation of an embodiment of this invention in connection with a trainstation with side tracks.

FIG. 2 a is a schematic illustration of a subway line in connection withwhich embodiments of the invention are applied.

FIG. 2 b is a plot illustrating the relative travel velocities of anexpress train and a local train along the subway line of FIG. 2 a,according to embodiments of this invention.

FIG. 3 a is an electrical diagram, in block form, illustrating acomputer system for scheduling and managing subway trains on the subwayline of FIG. 2 a, according to embodiments of the invention.

FIG. 3 b is a flow diagram illustrating the operation of the system ofFIG. 3 a in scheduling and managing subway trains on the subway line ofFIG. 2 a, according to embodiments of the invention.

FIGS. 3 c and 3 d are plots illustrating the relative travel velocitiesof express trains and local trains along the subway line of FIG. 2 a,according to embodiments of this invention.

FIGS. 3 e through 3 h are snapshot views of the subway line of FIG. 2 a,at specific points in time in the operation of that subway linedescribed in FIGS. 3 c and 3 d, according to embodiments of thisinvention.

FIGS. 4 a through 4 c and 4 e are schematic diagrams, in plan view, ofan express subway station enabling physical passing and directtrain-to-train passenger transfer according to an embodiment of theinvention.

FIG. 4 d is an elevation view of adjacent subway trains carrying outdirect train-to-train passenger transfer according to the embodiment ofthe invention shown in FIGS. 4 a through 4 c and 4 e.

FIGS. 5 a through 5 k are schematic diagrams, in plan view, of anexpress subway station enabling physical passing and directtrain-to-train passenger transfer according to embodiments of theinvention.

FIGS. 51 through 5 o are snapshot views at specific points in time inthe operation of the subway line described in 4 a through 4 d, accordingto embodiments of this invention.

FIG. 6 is a plot illustrating the relative travel velocities of trainstransforming between providing express service and local service along asubway line, according to embodiments of this invention.

FIGS. 7 a through 7 c are plots illustrating the operation of trainstransforming between providing express service and local service along asubway line, according to embodiments of this invention.

FIGS. 7 d through 7 g are snapshot views of the subway line of FIG. 2 a,at specific points in time in the operation of a subway line, accordingto conventional operation (FIG. 7 d) and to embodiments of thisinvention (FIGS. 7 e through 7 g).

FIGS. 8 a through 8 c are schematic diagrams, in plan view, illustratingthe operation of trains making a stop at an express station, accordingto an embodiment of the invention.

FIGS. 9 a through 9 c are schematic diagrams, in plan view, illustratingthe assignment of semi-express stations along an interval betweenexpress stations, according to an embodiment of the invention.

FIGS. 10 a through 10 g are schematic diagrams, in plan view,illustrating the operation of trains making a stop at an expressstation, according to another embodiment of the invention.

FIGS. 11 a through 11 c are schematic diagrams, in plan view,illustrating the operation of trains making a stop at an expressstation, according to another embodiment of the invention.

FIGS. 12 a through 12 h are schematic diagrams, in plan view,illustrating the operation of trains making a stop at an expressstation, according to other embodiments of the invention.

FIGS. 13 a and 13 b are plan and elevation views, respectively, of anexpress station at which the system of FIG. 3 a communicates boardinginstructions to passengers, according to embodiments of the invention.

FIGS. 13 c and 13 d are views of the content of graphics displays at thestation of FIGS. 13 a and 13 b by way of which boarding instructions arecommunicated to passengers, according to embodiments of the invention.

FIGS. 14 a through 14 d are timeline plots illustrating train traveltimes as varying spatially along a subway line, according to embodimentsof the invention.

FIGS. 15 a through 15 d are timeline plots illustrating train traveltimes as varying spatially along a subway line and varying with the timeof day, according to embodiments of the invention.

FIGS. 16 a through 16 d are timeline plots illustrating train traveltimes as varying spatially along a subway line, varying with the time ofday, and varying with the day of the week/month/year, according toembodiments of the invention.

FIGS. 17 a through 17 c are plots illustrating the elongation of expressstation intervals during non-rush hour periods, according to embodimentsof this invention.

FIG. 17 d illustrates the deployment of express stations for variousalternatives of scaling factors for non-rush hour periods, according toembodiments of this invention.

DETAILED DESCRIPTION OF THE INVENTION

This invention will be described in connection with its embodiments, asimplemented into an urban commuter rail system in which at least asignificant portion of the system is an underground subway system. Theseembodiments are described in this specification because it iscontemplated that this invention will be especially beneficial whenutilized in such an application. However, it is contemplated that thisinvention can also provide similar important benefits if implemented inother applications and environments. Accordingly, it is to be understoodthat the following description is provided by way of example only, andis not intended to limit the true scope of this invention as claimed.

FIG. 2 a schematically illustrates the context of embodiments of thisinvention in connection with subway line SLINE, which travels from anorigin to a terminus. For purposes of this contextual description,subway line SLINE will be discussed in connection with a singledirection of travel (west to east in FIG. 2 a); of course, subway lineSLINE in fact supports travel in both directions (west to east, and eastto west, in FIG. 2 a). In the example of FIG. 2 a, seven expressstations E0 through E6 are shown as located along subway line SLINE,with express station E0 corresponding to the origin, and express stationE6 corresponding to the terminus, of subway line SLINE in itswest-to-east direction of travel. As shown in FIG. 2 a, each ofintervals I1 through I6 is defined as the length of subway line SLINEbetween respective pairs of express stations E0 through E6 (e.g.,interval I1 is the interval between express stations E0 and E1, intervalI2 is the interval between express stations E1 and E2, and so on). Inthis example of subway line SLINE, local stations are present along eachinterval I1 through 16; for example, four local stations are locatedalong interval I1 between express station E0 and express station E1.Express stations E0 through E6 also serve as local stations(specifically, the local stations numbered 0, 5, 10, 15, etc. shown inFIG. 2 a), in this example.

FIG. 2 b illustrates the theoretical travel time for an express trainEXP and a local train LOC along subway line SLINE, in a single direction(e.g., west to east). The timing illustrated in FIG. 2 b shows expresstrain EXP and local train LOC leaving the origin of subway line SLINE(express station E0) at essentially the same time (0 minutes in FIG. 2b), but with express train EXP immediately leading local train LOC. Inthis example, local train LOC will stop at each local station along eachinterval I1 through I6 of subway line SLINE, while express train EXPstops only at express stations E1 through E6. Because express train EXPdoes not make the local stops while local train LOC does, express trainEXP reaches terminus express station E6 earlier than does local trainLOC. In this example, express train EXP reaches terminus E6 after thirtyminutes of travel, while local train LOC reaches terminus E6 after sixtyminutes of travel. Express train EXP may not necessarily be traveling atfaster instantaneous velocities along subway line SLINE than local trainLOC, but its higher effective travel velocity may result simply becauseit does not stop at the local (i.e., non-express) stations along subwayline SLINE. In any case, the overall travel time of express train EXPalong subway line SLINE is shorter than that of local train LOC.

However, if subway line SLINE is essentially a two-track line, such thatone railway track carries trains travelling in one direction and theother track carries trains travelling in the other direction, then thetheoretical timing illustrated in FIG. 2 b is valid only if expresstrain EXP does not catch up to any local train before reaching terminusE6. In the example of FIG. 2 b, this condition holds so long as no localtrain left origin express station E0 less than thirty minutes prior totime 0 at which express train EXP left origin express station E0.Otherwise, express train EXP would catch up to that earlier-leavinglocal train, and its travel velocity from that point forward would belimited by the travel velocity and local station stops of thatearlier-leaving local train. In other words, because subway line SLINEis a two-track line, a faster traveling express train is unable to passa slower moving local train. To avoid this situation of express trainsbeing limited by local train service, trains must be separated farenough in time that no express train can catch up to the immediatelypreceding local train. Of course, it is generally impractical to operatea subway system of any length or ridership level in which trains areseparated by such long times, for example no less than thirty minutes asin the case of FIG. 2 b.

Because of this limitation, most conventional two-track lines in modernsubway systems do not support express train service. Rather, every trainalong these conventional subway lines operates as a local train, and thepassenger throughput and travel convenience are limited—every subwaypassenger must endure the time required for the train to make everylocal stop along his or her trip. Typically, the cost of providing sidetracks as described above relative to FIG. 1 a is prohibitive in thesubway context, especially if a subway operator wishes to retrofit anexisting two-track station to provide express service (for example, toalleviate overcrowding of trains in local-only service).

It has been discovered, according to this invention, that express subwayservice can be provided within a two-track system, in a manner thatrequires, at most, a much reduced cost relative to the cost ofretrofitting stations to include conventional side tracks; in someembodiments of this invention, as will become apparent from thefollowing description, express service can be provided in a subwaysystem without incurring any construction or infrastructure costs. Thisinvention thus provides important benefits to both the subway operatorand the subway passenger community, such benefits including improvedpassenger throughput that results in reduced passenger travel times andreduced passenger overcrowding, improved utilization of existing subwayinfrastructure, and enhanced passenger autonomy in managing subwaytravel.

Synchronization of Express and Local Trains

As evident from the previous description, in order to provide reasonableexpress subway service on a two-track subway line (i.e., one track foreach direction of travel), the ability of an express train toeffectively pass a slower traveling local train must be provided. Asmentioned above, it is contemplated that express subway trains may notactually be traveling at faster instantaneous velocities than localtrains, but may instead travel at faster effective travel velocitiesbecause these express train do not stop at local (i.e., non-express)stations.

According to embodiments of the invention, express stations areperiodically defined as locations along a subway line at which expresssubway trains and local subway trains both make stops, at whichpassengers may board and de-board both local and express trains, and atwhich passengers may transfer from a local train to an express train.Also according to embodiments of the invention, the scheduling of theexpress and local trains is synchronized relative to each other so thatthe faster-traveling express trains catch up to slower-traveling localtrains at express stations only. And at those express stations, expresstrains are permitted to pass local trains, either physically or“virtually”, even though the subway line may be constructed as atwo-track subway line with only one track provided for travel in eachdirection. The particular manner in which the physical or virtualpassing of trains is carried out at these stations will be described indetail below in connection with the specific embodiments of thisinvention.

According to embodiments of this invention, the scheduling of theexpress and local trains to arrive effectively simultaneously at expressstations is carried out by a computerized system that is constructed,programmed, and operated to accomplish that scheduling task. FIG. 3 aillustrates, according to an example of an embodiment of the invention,the construction of subway scheduling and operating system (“system”)20. In this example, system 20 is as realized by way of a computersystem including workstation 21 connected to server 30 by way of anetwork. Of course, the particular architecture and construction of acomputer system useful in connection with this invention can varywidely. For example, system 20 may be realized by a single physicalcomputer, such as a conventional workstation or personal computer, oralternatively by a computer system implemented in a distributed mannerover multiple physical computers. Accordingly, the generalizedarchitecture illustrated in FIG. 3 a is provided merely by way ofexample.

As shown in FIG. 3 a and as mentioned above, system 20 includesworkstation 21 and server 30. Workstation 21 includes central processingunit 25, coupled to system bus BUS. Also coupled to system bus BUS isinput/output interface 22, which refers to those interface resources byway of which peripheral functions P (e.g., keyboard, mouse, display,etc.) interface with the other constituents of workstation 21. Centralprocessing unit 25 refers to the data processing capability ofworkstation 21, and as such may be implemented by one or more CPU cores,co-processing circuitry, and the like. The particular construction andcapability of central processing unit 25 is selected according to theapplication needs of workstation 21, such needs including, at a minimum,the carrying out of the functions described in this specification, andalso including such other functions as may be executed by computersystem 20. In the architecture of system 20 according to this example,system memory 24 is coupled to system bus BUS, and provides memoryresources of the desired type useful as data memory for storing inputdata and the results of processing executed by central processing unit25. According to this embodiment of the invention, workstation 21 alsoincludes program memory 34, which is a computer-readable medium thatstores executable computer program instructions according to which theoperations described in this specification are carried out. In thisembodiment of the invention, these computer program instructions areexecuted by central processing unit 25, for example in the form of aninteractive application, to generate schedules for the express and localtrains that are to travel on subway line SLINE, and in some instances,to manage the operation of subway line SLINE according to that scheduleand in response to actual conditions encountered during operation. Thesecomputer program instructions can result in data and results that aredisplayed or output by peripherals I/O in a form useful to the humanuser of workstation 21, or that result in operational signals to becommunicated to the trains and stations. Of course, this memoryarrangement is only an example, it being understood that the particulararrangement and architecture of memory resources within workstation 21may vary, for example by implementing data memory and program memory ina single physical memory resource, or distributed in whole or in partoutside of workstation 21.

Network interface 26 of workstation 21 is a conventional interface oradapter by way of which workstation 21 accesses network resources on anetwork. In this embodiment of the invention, the network to whichnetwork interface 26 is coupled may be a local area network, or may be awide-area network such as an intranet, a virtual private network, or theInternet. As shown in FIG. 3 a, one or more of the network resourcesaccessible by workstation 21, either directly or indirectly, includestrain/station interface 28 that receives inputs via bus TRN_I/O from orconcerning each of the subway trains in subway line SLINE (or throughoutthe subway system including subway line SLINE), that receives inputs viabus STA_I/O from or concerning each of the subway stations along subwayline SLINE (or throughout the subway system including subway lineSLINE), and that also communicates signals to those subway trains andstations via buses TRN_I/O and STA_I/O. The signals communicated fromthese trains and stations are received by interface 28 and, in thisexample, are stored in a memory resource that resides locally withinworkstation 21, or that is accessible to workstation 21 over thenetwork, via network interface 26.

As shown in FIG. 3 a, the network resources to which workstation 21 hasaccess via network interface 26 also include server 30, which resides ona local area network, or a wide-area network such as an intranet, avirtual private network, or the Internet, and which is accessible toworkstation 21 by way of one of those network arrangements and bycorresponding wired or wireless (or both) communication facilities. Inthis embodiment of the invention, server 30 is a computer system, of aconventional architecture similar, in a general sense, to that ofworkstation 21, and as such includes one or more central processingunits, system buses, and memory resources, network interface functions,and the like. In addition, library 32 is also available to server 30(and perhaps workstation 21 over the local area or wide area network),and stores such archival or reference information as may be useful insystem 20. Library 32 may reside on another local area network, oralternatively be accessible via the Internet or some other wide areanetwork. It is contemplated that library 32 may also be accessible toother associated computers in the overall network.

Of course, the particular memory resource or location at whichpersistent and temporary data, library 32, and program memory 34physically reside can be implemented in various locations accessible tothe computational resources of system 20. For example, data and programinstructions may be stored in local memory resources within workstation21, within server 30, or in memory resources that are network-accessibleto these functions. In addition, each of the data and program memoryresources can itself be distributed among multiple locations, as knownin the art. It is contemplated that those skilled in the art will bereadily able to implement the storage and retrieval of the applicablemeasurements, models, and other information useful in connection withthis embodiment of the invention, in a suitable manner for eachparticular application.

According to this embodiment of the invention, program memory withinsystem 20, whether within workstation 21 or within server 30, storescomputer instructions that are executable by computational functionswithin central processing unit 25 and server 30, respectively, to carryout the functions described in this specification, by way of which thedeparture and operation of subway trains traveling along subway lineSLINE are scheduled and managed. These computer instructions may be inthe form of one or more executable programs, or in the form of sourcecode or higher-level code from which one or more executable programs arederived, assembled, interpreted or compiled. Any one of a number ofcomputer languages or protocols may be used, depending on the manner inwhich the desired operations are to be carried out. For example, thesecomputer instructions may be written in a conventional high levellanguage, either as a conventional linear computer program or arrangedfor execution in an object-oriented manner. These instructions may alsobe embedded within a higher-level application. For example, thescheduling and operation applications can reside entirely within programmemory 34 of workstation 21, such that workstation 21 itself executesthe method and processes described in this specification in connectionwith the embodiments of this invention, with server 30 performingnetwork and data retrieval operations. According to another example, anexecutable web-based application can reside at program memory withinserver 30 and client computer systems such as workstation 21, receiveinputs from the client system in the form of a spreadsheet, executealgorithms modules at a web server, and provide output to the clientsystem in some convenient display or printed form, or output to trainsand stations by way of signals communicated via interface 28. Otherarrangements may of course also be constructed and operated within asystem architecture such as that of system 20 shown in FIG. 3 a, oraccording to other architectures. It is contemplated that those skilledin the art having reference to this description will be readily able torealize, without undue experimentation, this embodiment of the inventionin a suitable manner for the desired installations. Alternatively, thesecomputer-executable software instructions may be resident elsewhere onthe local area network or wide area network, or downloadable fromhigher-level servers or locations, by way of encoded information on anelectromagnetic carrier signal via some network interface orinput/output device. The computer-executable software instructions mayhave originally been stored on a removable or other non-volatilecomputer-readable storage medium (e.g., a DVD disk, flash memory, or thelike), or downloadable as encoded information on an electromagneticcarrier signal, in the form of a software package from which thecomputer-executable software instructions were installed by system 20 inthe conventional manner for software installation.

Referring now to FIG. 3 b, the generalized operation of system 20 incarrying out the scheduling and operation of subway line SLINE, and itstrains and stations, according to this invention will be described. Thespecific operations involved in connection with the embodiments of thisinvention will, of course, vary from embodiment to embodiment, and willbe apparent to those skilled in the art having reference to thisspecification. However, it is contemplated that the generalizedoperation illustrated in FIG. 3 b will provide context for the manner inwhich the automated and computerized control can be realized, in amanner that is well-suited for providing the benefits of this invention.

The generalized flow diagram of FIG. 3 b illustrates that the overallschedule and deployment of express and subway trains according to thisembodiment of the invention is based on various sources of data andinformation, all of which are stored in library 32 or some other memoryresource of system 20. Passenger data source 33 includes data regardingthe number of passengers using subway line SLINE, data regarding thenumbers of passengers that embark and disembark subway line SLINE ateach of the various stations along the line, data regarding how thosenumbers of passengers vary relative to the time of day and also from dayto day, and other similar data that may be useful in defining a subwaytrain line schedule. Train data source 35 includes data indicating thenumber of subway trains and cars available for subway line SLINE, thenumber of passengers each train and car can carry comfortably or safely(or both, should those numbers differ from one another), data regardingthe maximum and optimal (desired) velocities at which the trains andcars can travel along a subway line, stopping distances, and othersimilar data regarding the train resources that may be useful indefining a subway train schedule. Station data source 37 include dataindicating the locations of stations along subway line SLINE, theinfrastructure attributes of each of those stations (e.g., length ofplatform, passenger handling capacity, presence of supportinfrastructure, etc.), whether connections to other subway lines arelocated at those stations and the passenger demand for such connections,and other similar data regarding the stations along subway line SLINEthat may be useful in defining a subway train schedule. Data from thesedata sources 33, 35, 37, as well as data regarding other parametersuseful to the scheduling process, are accessed or otherwise available tosystem 20 in carrying out the scheduling process of embodiments of theinvention.

In this high-level description of FIG. 3 b, process 34 is carried out bysystem 20 to define which stations along subway line SLINE are to beexpress and local stations, and which stations are to be local stationsonly. In some cases, the selection of express stations along subway lineSLINE may be pre-determined based on other criteria, such as by uppermanagement of the subway station, the manner in which the particularstations may be constructed (to the extent not represented withinstation data source 37), customer surveys, or the like. Absent suchexternal restrictions, process 34 is performed by computationalresources within system 20 executing program instructions to optimizethe selection of express stations, for example in an automated or“artificial intelligence” manner. For example, operational criteria maybe used to define a cost function, such that iterative or Monte Carloevaluation of the cost function may be performed using a number of trialselections of express stations, in order to evaluate the optimumassignment based on passenger data 33, train data 35, and station data37. Preferably, parameters representative of passenger throughput,passenger travel time, passenger comfort (i.e., avoiding overcrowdedconditions), and subway train utilization, will be reflected in such acost function. It is contemplated that those skilled in the art havingreference to this specification will be able to apply conventional AIand other evaluation techniques to define the express stations for thecurrent information, in this process 34.

In process 36, computational resources within system 20 execute programinstructions to define the number and frequency of express and localtrains to be scheduled along subway line SLINE over time within a day,and as that schedule may vary from day to day. Similarly as process 34described above, it is contemplated that process 36 is also carried outin an automated manner, for example by evaluating a cost function thatexpresses criteria involved in defining the numbers, lengths, andarrangement of express trains within the schedule. As will be evidentfrom some embodiments of this invention described below, definitionprocess 36 can include the defining of “group” subway trains, with theexpress portion substantially longer than the local portion. Constraintson the number of express trains are contemplated to depend on thevarious data elements described above and provided from data sources 33,35, 37. Preferably and as described above, parameters representative ofpassenger throughput, passenger travel time, passenger comfort (i.e.,avoiding overcrowded conditions), and subway train utilization, will bereflected in the cost function that is optimized in process 36. It iscontemplated that those skilled in the art having reference to thisspecification will be able to apply conventional AI and other evaluationtechniques to define the number and frequency of express trains for thecurrent information relative to subway line SLINE, in this process 36.

Alternatively to processes 34, 36, the definition of express stationsand the numbers and frequencies of express trains can instead be defineda priori by subway system management. While it is contemplated that suchdefinition of these resources will, in general, not be optimized for allof the objectives of passenger throughput, passenger travel time,passenger comfort, and subway train utilization, and the like, theoverall scheduling and operational process of this invention can stilloperate within such an environment to optimize these and otherattributes within those constraints.

In process 38, computational resources within system 20 operate toderive a schedule for subway line SLINE over time, for the expressstations defined in process 34 (or otherwise) and for the number andfrequency of express trains defined in process 36 (or otherwise).According to embodiments of this invention, the schedule derived inprocess 38 synchronizes the operation of express and local trains sothat express and local trains meet in time only at express stations. Asmentioned above and as will be evident from the following description ofembodiments of this invention, express stations allow for express trainsto pass the slower-traveling local trains, either physically orvirtually; conversely, at locations other than express stations alongsubway SLINE, an express train that catches up to a local train willhave its travel time constrained by the speed of and stops made by thelocal train, at least until both trains reach the next express station.Optimal operation of subway line SLINE is thus contemplated to beachieved with express and local trains traveling in the same directionmeeting only at express stations; in process 38, as a result, thedepartures and travel velocities of express trains will be defined in amanner that is synchronized with the schedule being followed by thelocal train that is ahead of the express train along subway line SLINE.It is contemplated that those skilled in the art having reference tothis specification will be able to apply conventional AI and otherevaluation techniques, for example by evaluating a cost function thatexpresses criteria involved in deriving the schedule, to define theoperational schedule of subway line SLINE, including departure times andtravel velocities, for the current information relative to subway lineSLINE, in this process 38. In such an example, the cost function mayexpress some measure related to passenger travel time along subway lineSLINE, in an average, cumulative, or some other statistical sense, suchthat the schedule is derived, in process 38, by minimizing this measureof passenger travel time.

Referring to FIG. 3 c, the manner in which express and local trains aresynchronized with one another in an optimal schedule derived in process38, according to embodiments of this invention, will now be described.FIG. 3 c is a plot of train travel along subway line SLINE, presented ina form in which distance follows the horizontal axis and time followsthe vertical axis (increasing time in the downward direction). Thetravel of express trains EXP1 through EXP4 and local trains LOC0 throughLOC3 along subway line SLINE is illustrated in FIG. 3 c. As evident fromFIG. 3 c, express trains EXP1 through EXP4 travel at effectively twicethe travel velocity of local trains LOC0 through LOC3, in large partbecause local trains LOC0 through LOC3 stop at local stations (notshown) between express stations. This difference in speed of coursemeans that faster express trains EXP1 through EXP4 will catch up toslower local trains LOC0 through LOC3 at some point along subway lineSLINE. But because subway line SLINE is a two-track line, one track ineach direction of travel, some provision must be made to allow expresstrains EXP1 through EXP4 to make passes.

According to embodiments of this invention, express trains EXP1 throughEXP4 are synchronized with local trains LOC0 through LOC3 in the sensethat express trains EXP1 through EXP4 catch up to local trains LOC0through LOC3 only at express stations E0 through E3. For example, localtrain LOC1 leaves express station E0 at an earlier time (time t1) thanexpress train EXP2 leaves express station E0 (time t2), yet both arriveat express station E1 at the same time (time t3). Similarly, expresstrain EXP3 catches up to the next previous local train LOC0 at expressstation E2 (at time t4). The other trains traveling along subway lineSLINE proceed in a similar manner. Of course, in order for the scheduleof FIG. 3 c to hold, provision must be made for express trains EXP1through EXP4 to pass local trains LOC0 through LOC3. As such, in theschedule of FIG. 3 c, pass points 1P10 through 1P43 are shown in FIG. 3c as occurring at express station E1 (e.g., pass point “1P10” expressingthat at express station E1, express train EXP1 is passing local trainLOC0), at times t2 through t5. Similarly, FIG. 3 c shows pass points2P20 through 2P42 occurring at express station E2, and pass point 3P30occurring at express station E3. Each of the pass points 1P10 etc. inFIG. 3 c should be considered as “space-time” points, as they eachindicate a particular spatial point at a particular time (e.g., passpoints 1P10 and 1P21 are at the same point in space, namely expressstation E1, but at different times t2, t3, respectively).

While the time scale and distance scale are shown as constant along theaxes in FIG. 3 c, such that express stations E0 through E3 (and timeintervals t1 through t6) appear at uniform intervals relative to oneanother, it is to be understood that such uniformity is not necessarilythe case. As such, in the actual operation of the schedule of subwayline SLINE as shown in FIG. 3 c, express trains EXP1 through EXP4 andlocal trains LOC0 through LOC3 do not necessarily travel at a constantvelocity. Rather, in order for the synchronized arrival of expresstrains EXP1 through EXP4 and local trains LOC0 through LOC3 only atexpress stations E1 through E3, as shown in FIG. 3 c, it may benecessary for the instantaneous velocities of these trains to vary frominterval to interval. In particular, embodiments of this inventioncontemplate that the instantaneous velocity of express trains EXP1through EXP4 will vary from interval to interval so that their arrivaltimes at express stations E1 through E3 are synchronized with those oflocal trains LOC0 through LOC3.

FIG. 3 d illustrates the case in which the distance (either in miles orin number of intervening local stops, or both) between express stationsvaries from interval to interval. For example, the time axis of FIG. 3is at a constant scale along its length, by way of constant intervals Δtbetween each time point, however the distance intervals vary betweenexpress stations. In this example, interval I₃ between express stationsE2 and E3 is longer than interval I₂ between express stations E1 and E2,however. In this case, the average velocity of a local train travelingfrom express station E0 to express station E3 is the same as that inFIG. 3 c (i.e., local train LOC0 leaves express station E0 at time t=0and arrives at express station E3 at time t6), as is the averagevelocity of an express train (i.e., express train EXP3 leaves expressstation E0 at time t3 and arrives at express station E3 at time t6).However, within the various intervals, the interval velocity of eachexpress train is governed by the interval velocity of a local trainahead of that express train over that interval.

FIG. 3 d illustrates this governing relationship, relative to localtrain LOC0. In this example, an express train leaves express station E0at the end of each time interval Δt following time t=0, followedimmediately by a local train as before. The interval velocity of localtrain LOC0 over the first express interval I₁ will depend on variousfactors such as the instantaneous velocities at which local train LOC0travels between stops, the stop time at each local station over theinterval, and the like. In any event, the interval velocity of the nextexpress train EXP1 over express interval I₁ is governed by the intervalvelocity of local train LOC0 over that distance, such that express trainEXP1 meets and passes local train LOC0 at express station E1 (pass point1P10), and therefore leaves express station E1 before local train LOC0.Over the next shorter interval I₂ from express station E1 to expressstation E2, local train LOC0 travels at its interval velocity, which inthis example is slightly faster than its interval velocity over intervalI₁ (as evidenced by the slightly flatter line in the plot of FIG. 3 dover this interval). The interval velocity of express train EXP2 overinterval I₂ is governed by the interval velocity of local train LOC0over this interval; as evident from FIG. 3 d, this interval velocity isalso faster than its interval velocity over interval I₁ so as to meetand pass local train LOC0 at express station E2 (pass point 2P20).Express train EXP 2 leaves express station E2 ahead of local train LOC0in this example, so that local train LOC0 leads express train EXP3 overthe next interval I₃. Over that interval I₃, the interval velocity oflocal train LOC0 increases further in this example (as evidenced by theflatter line in the plot of FIG. 3 d for local train LOC0 over thisinterval I₃); the interval velocity of express train EXP3 also increasesover interval I₃, so that express train EXP3 meets local train LOC0 atexpress station E3 at time t6 as shown. As such, it is the velocity oflocal trains LOC along subway line SLINE that governs the velocity ofthe following express trains EXP, so that the synchronized meeting andpassing of express and local trains occurs only at express stations,according to embodiments of this invention.

This operation of subway line SLINE according to embodiments of thisinvention can be further described in connection with the schematicviews of subway line SLINE shown in FIGS. 3 e through 3 h. These FIGS. 3e through 3 h can be considered as plan views, as though looking down onsubway line SLINE from above (and through the earth above subway lineSLINE). FIG. 3 e illustrates the state of subway line SLINE at a pointin time in which local trains T0 through T6 are located along subwayline SLINE between express stations E0 and E3, with the first localtrain T0 at express station E3 and local train T6 at the farthest-westexpress station E0. At the point in time shown in FIG. 3 e, expresstrain {circumflex over (T)}0 is beginning the trip along subway lineSLINE, at express station E0. At the snapshot in time shown in FIG. 3 e,local train T5 is located between express stations E0 and E1, localtrain T3 is located between express stations E1 and E2, and local trainT1 is located between express stations E2 and E3.

FIG. 3 f illustrates subway line SLINE at the point in time at whichlocal train T0 has reached express station E6. In other words, in timebetween that shown in FIG. 3 e and that shown in FIG. 3 f, local trainT0 (and all other local trains) have traveled the distance of threeexpress intervals. Meanwhile, during this same time interval, expresstrain {circumflex over (T)}0 has traveled six express intervals, and assuch has caught up to local train T0 at express station E6. At theexpress stations E1 through E5 encountered by express train {circumflexover (T)}0 during this time, express train {circumflex over (T)}0 passedone of local trains T5 through T1, respectively. During this same timeinterval, the pair of express train {circumflex over (T)}1 and localtrain T7 were dispatched from express station E0 at a time delay Δtfollowing the departure of express train {circumflex over (T)}0 andlocal train T6. Express train {circumflex over (T)}2 and local train T8left express station E0 at time 2Δt after trains {circumflex over (T)}0and T6 departed, trains {circumflex over (T)}2 and T8 departed at time3Δt after trains {circumflex over (T)}0 and T6 departed, and so on up tothe pair of express train {circumflex over (T)}5 and local train T11departing express station E0 after a time delay of 5Δt after trains{circumflex over (T)}0 and T6 departed. During the interval between thesnapshot of FIG. 3 e and that of FIG. 3 f, each of express trains{circumflex over (T)}1 through {circumflex over (T)}5 have passed orcaught up to corresponding local trains T2 through T11. At the timeshown in FIG. 3 f, express train {circumflex over (T)}6 and local trainT12 are at express station E0 and ready to depart.

FIG. 3 g illustrates the portion of subway line SLINE from expressstation E0 through express station E3, at the time corresponding to thatshown in FIG. 3 f, in more detail. The point in time shown in FIG. 3 gcorresponds to that at which the express trains {circumflex over (T)}3through {circumflex over (T)}6 have not yet passed their respectivelocal trains T6 through T12, respectively. As evident in FIG. 3 g,express trains {circumflex over (T)}3 through {circumflex over (T)}6arrive at express stations E0 through E3 shortly after the local trainsT6, T8, T10, T12 that they are passing, respectively. FIG. 3 hillustrates the same situation as shown in FIG. 3 g, except in the casein which the distances between express stations E0 through E3 is notuniform (i.e., as in the plot of FIG. 3 d). As evident in FIG. 3 h, thissituation is managed by modulating the interval velocities of thetrains, as described above.

In connection with this invention, scheduling process 38 derives aschedule in which express trains and local trains meet one another, whentraveling in the same direction, only at express stations. It iscontemplated that the manner in which scheduling process 38 is executedcan readily define and optimize the schedule by selecting and modulatingthe departure times and travel velocities of the express trains asgoverned by the departure times and travel velocities of the localtrains. Conventional computer operations are contemplated to be readilycapable of performing such optimization, given the constraints presentedby the synchronization requirements of embodiments of this invention.The manner in which express trains physically or virtually pass thelocal trains at each of the pass points P in FIG. 3 c will be describedin detail in this specification, in connection with the particularembodiments.

Referring back to FIG. 3 b, according to this generalized method, it iscontemplated that the schedule derived in process 38 may be able to befurther optimized by changing the relative densities of express andlocal trains along subway line SLINE, or even by redesignating somestations as express stations or as local stations, as the case may be.As such, and as shown in FIG. 3 b, further iterations of processes 34,36 may be performed in light of the optimal schedule derived in the mostrecent instance of process 38. It is contemplated, therefore, that thoseskilled in the art having reference to this specification will be ableto comprehend such iteration in their particular arrangement of theoverall process, again according to conventional optimizationtechniques.

It is contemplated that processes 34, 36, 38 shown in FIG. 3 b will becarried out to derive an operational schedule under one set of operatingconditions, for example the high demand conditions of “rush hour”commute periods, as such periods are especially challenging foroperation of subway lines in modern urban environments. According toanother embodiment of this invention, FIG. 3 b illustrates optionalprocess 39, in which a second schedule is derived for use in non-rushhour time periods. It is contemplated, as will be described in furtherdetail below, that passenger data 33, train data 35, and station data 37may indicate that the optimization of the operating schedule may differgreatly in such non-rush hour periods than during rush hour periods. Assuch, according to that alternative embodiment of the invention, it maybe advantageous from the standpoint of train utilization efficiency andalso passenger convenience.

In process 40, the results of the final instance of processes 38, 38′are communicated to passengers. It is contemplated that process 40 canbe carried out in various ways, including the generation of printedschedules, online schedules, push-transmissions to Internet-capabledevices, and the like. It is also specifically contemplated, inconnection with embodiments of this invention, that the derived schedulewill be communicated to passengers, in process 40, by way of videodisplays at stations along subway line SLINE, and video displays on thetrains themselves. To the extent that communication process 40 isperformed electronically, for example to stations and trains, it iscontemplated that system 20 will provide those communications viatrain/station interface 28 (FIG. 3 a) and buses STA_I/O and TRN_I/O.According to another example, it is contemplated that interactive“e-tickets” may be sold and communicated by the subway operator,enabling real-time communication with passengers regarding scheduling,car and platform assignments, and the like. The particular manner inwhich the schedule is communicated to passengers in process 40 can, ofcourse, vary widely and may take any or all of these approaches and alsothose communications technologies that may be developed in the future.

Also as shown in FIG. 3 b, according to this generalized method, it iscontemplated that, during operation, the conditions along subway lineSLINE may require changes in the schedule of one or more trains inmid-course, or for the remainder of the day. Data regarding the currentreal-time status of trains and stations along subway line SLINE areacquired by system 20, for example via buses STA_I/O, TRN_I/O andstation/train interface 28. In this generalized operation of embodimentsof this invention, operational data 41 are communicated in this manneror otherwise to system 20, and in process 42, computational resourceswithin system 20 execute program instructions to adjust departure timesand running velocities of trains along subway line SLINE to optimize itsoperation, in light of the previous optimization and the currentconditions. For example, system 20 may receive inputs corresponding tothe current location and status of each of the trains along subway lineSLINE at a given instant in time and can compare that feedback data toexpected or desired locations and status of the trains according to thecurrent schedule; the error between the actual and expected positions ofthe train along subway line SLINE can then indicate the nature andmagnitude of changes to be made to the operation of the trains, forexample by modulating instantaneous velocities of one or more of thetrains, or by adjusting the stop times of one or more of the trains atone or more of the stations along subway line SLINE. As shown in FIG. 3b, such adjustments are then used in another instance of process 40, sothat the changes in the schedule are communicated as appropriate toaffected and potentially affected passengers.

System 20 and its operation, as described above in connection with FIGS.3 a and 3 b, are presented in this specification by way of example, andin a generalized manner. It is contemplated that many variations andalternatives to this system and its operation as described above will beapparent to those skilled in the art having reference to thisspecification, in their implementation of this invention in particularinstallations. It is contemplated that such variations and alternativeswill be within the scope of this invention as claimed.

Conventional Side-Track Subway Station

According to an embodiment of the invention, the synchronized schedulingof express and local subway trains, as described above in connectionwith FIGS. 3 a through 3 h, can be implemented for subway lines havingconventional side-track facilities at express stations, suchconventional side-track facilities described above in connection withFIG. 1 a. Referring now to FIGS. 1 b through 1 d, an example of theoperation of an embodiment of the invention in connection with such aconventional side-track station will now be described.

FIG. 1 b illustrates express station E_(x) at a point in time in whichan earlier-arriving eastbound local train LOC₀ has arrived at stationE_(x), and has switched over to side-track 4WE, at which time passengersmay board and de-board local train LOC₀ via platform 5WE. While localtrain LOC₀ is stopped at platform 5WE in this manner, later arrivingexpress train EXP₀ arrives at platform 5WE along track 2WE, as shown inFIG. 1 c. At the point in time shown in FIG. 1 c, passengers can boardand de-board express train EXP₀ from platform 5WE; in addition,passengers can transfer between local train LOC₀ and express train EXP₀via platform 5WE, as shown. Following the time required for thisboarding and transfer process, express train EXP₀ then leaves expressstation E_(x) ahead of local train LOC₀, as shown in FIG. 1 d; in thismanner, express train EXP₀ physically passes local train LOC₀ at expressstation Ex. In addition, if the express passenger demand is sufficientthat multiple express trains are scheduled to pass local train LOC₀ atthis station E_(x) (such multiple-express train groups will be describedin further detail below), another express train EXP₁ can also arrive atplatform 5WE while local train LOC₀ remains stopped along side track 4WEas shown in FIG. 1 d. In this manner, this additional express train EXP₁can also pass local train LOC₀, and allow passenger to and from localtrain LOC₀ and from platform 5WE in the manner illustrated in FIG. 1 c.

Synchronization of the express and local train schedules so that expresstrains EXP catch up to local trains LOC only at express stations, asdescribed above in connection with FIGS. 3 a through 3 h, ensures theshortest possible travel times for the express trains EXP along subwayline SLINE, while optimizing the use of local trains LOC and minimizingpassenger wait times for those making transfers between the trains atexpress stations. It is contemplated that this embodiment of theinvention will thus improve the utilization of existing subway train andstation infrastructure, by increasing the passenger throughput of thesubway line. In addition, as passenger throughput increases and expresspassenger travel times decrease, it is contemplated that overcrowding ofthe subway trains can be reduced, if not eliminated, through thesynchronization method of this invention.

Side-by-Side Subway Station

As described above in connection with FIGS. 1 b through 1 d, embodimentsof this invention can be used with side track stations of conventionalconstruction to enable express trains to physically pass local trainsalong a two-track subway line. However, it is believed that few existingsubway stations in the world provide side-track facilities such as thoseshown in FIGS. 1 b through 1 d. It is also believed, as described above,that the cost of retro-fitting (or originally constructing) subwaystations to have such conventional side-tracks is prohibitive. Inaddition, the passenger transfer times at such stations, via theintervening platform, is contemplated to be significant at theseconventional side-track equipped stations.

According to another embodiment of the invention, the express subwaystations are constructed so that direct train-to-train passengertransfers are possible, reducing the duration of express station stoptimes and also minimizing the footprint of the express station (and thusthe construction or retrofit cost). In addition, according to thisembodiment of the invention, the ability for an express subway train topass a local subway train, and to permit passengers to transfer directlybetween the local and express trains, is facilitated. As describedabove, the scheduling of the express and local trains is synchronizedrelative to each other so that the faster-traveling express trains catchup to slower-traveling local trains at express stations only; at thoseexpress stations, the express trains are permitted to pass local trains.

FIGS. 4 a through 4 e illustrate an example of express subway stationE_(x) on subway line SLINE constructed according to one embodiment ofthe invention in which passenger transfers occur at a location beyondthe station platform. FIG. 4 a is a plan view of express station E_(x),at which eastbound and westbound platforms 50 e, 50 w, respectively, areprovided for passenger boarding and de-boarding. Main track 52 e foreastbound trains and main track 52 w for westbound trains pass betweenplatforms 50 e, 50 w, and are adjacent to their respective platforms 50e, 50 w. Side track 54 e is provided adjacent to main track 52 e at thelocation of station E_(x), and abuts the end of platform 50 e as shown;side track 54 e couples to main track 52 e in both directions, as shown,under the control of conventional switches (not shown). Similarly, sidetrack 54 w is provided adjacent to main track 52 w at station E_(x),abutting the end of platform 50 w; side track 54 w also couples to maintrack 52 w in both directions.

FIG. 4 b illustrates station E_(x) in operation, according to thisembodiment of the invention, at a time that eastbound local train LOC₀and eastbound express train EXP₀ are stopped at station E_(x). In thisexample, local train LOC₀ arrived at station Ex before express trainEXP₀, considering that the effective travel velocity of express trainEXP₀ is faster than that of local train LOC₀ according to embodiments ofthis invention, as described above. Earlier-arriving local train LOC₀has pulled onto side-track 54 e at station E_(x), and has backed up(westward) by a small distance so that its trailing end is at or nearthe end of platform 50 e (FIG. 4 c illustrates an expanded view of thisarea of express station E_(x) with local train LOC₀ and express trainEXP₀ stopped thereat). Meanwhile, the later-arriving express train EXP₀has stopped at station E_(x), but remains on main track 52 e; as will beevident from this description, express train EXP₀ will depart station Exon main track 52 e ahead of local train LOC₀, to effect its pass oflocal train LOC₀ along subway line SLINE.

As shown in FIG. 4 b, express train EXP₀ in this example is twice aslong than local train LOC₀. More specifically, express train EXP₀ has afront half EXP_(0,F) that is about the length of local train LOC₀, and arear half EXP_(0,R). At the time that both express train EXP₀ and localtrain LOC₀ are stopped at express station E_(x), front half EXP_(0,F) isstopped adjacent to local train LOC₀, and rear half EXP_(0,R) is stoppedadjacent to platform 50 e. FIG. 4 c illustrates this position of trainsEXP₀, LOC₀, and platform 50 e in further detail. Local train LOC₀consists of n coupled cars, with the rear-most car LOC₀(n) abuttingplatform 50 e, and cars LOC₀(n−1), LOC₀(n−2), etc. in sequence ahead ofrear-most car LOC₀(n). Similarly, front half EXP_(0,F) of express trainEXP₀ consists of m coupled cars, with the rear-most car EXP_(0,F)(m)stopped adjacent to local train car LOC₀(n), and cars EXP_(0,F)(m−1),EXP_(0,F)(m−2), etc. in sequence ahead of rear-most car EXP₀(m) andadjacent to corresponding cars LOC₀(n−1), LOC₀(n−2), etc. of local trainLOC₀. Rear half EXP_(0,R) of express train EXP₀ is stopped adjacent toplatform 50 e, as described above, with its front-most car EXP_(0,R)(1)shown in FIG. 4 c. Trailing cars EXP_(0,R)(1) et seq. (not shown) arecoupled in sequence behind front-most car EXP_(0,R)(1) to complete rearhalf EXP_(0,R). Front-most car EXP_(0,R)(1) is also coupled to thetrailing end of rear-most car EXP_(0,F)(m), to keep front half EXP_(0,F)and a rear half EXP_(0,R) as a unitary express train EXP₀.

As shown in FIG. 4 d, according to this embodiment of the invention,distance D_(st) between main track 52 e and its side track 54 e (showncenter-line to center-line in FIGS. 4 b and 4 d) is selected so thatadjacent cars of local train LOC₀ and express train EXP₀, when both arestopped at station E_(x), are sufficiently close together to allowpassengers to transfer directly between the two trains LOC₀, EXP₀. Ofcourse, side doors of adjacent cars of trains LOC₀, EXP₀ must be alignedwith one another to permit such passenger transfer. FIG. 4 cschematically illustrates the paths of passenger movement between trainsLOC₀, EXP0. Similarly, main track 52 e is positioned sufficiently closeto platform 50 e that passengers can safely and easily board andde-board express train EXP₀ when stopped at the platform, as shown inFIG. 4 c with respect to car EXP_(0,R)(1).

FIG. 4 d illustrates, by way of an elevation view, that local train carLOC₀(n) is positioned sufficiently close to adjacent express train carEXP_(0,F)(n) that passengers can easily step over separation distanceD_(sep) between cars LOC₀(n) and EXP_(0,F)(n), and vice versa. It iscontemplated that separation distance D_(sep) is on the order of thedistance between platform 50 e and cars in express train rear halfEXP_(0,R). In any event, this separation distance D_(sep) iscontemplated to be significantly smaller than separation distanceD_(trv) between trains passing in opposite directions on main tracks 52,52 w, as shown in FIG. 4 d; that separation distance D_(trv) iscontemplated to be at least as wide as the minimum specified separationbetween passing trains at any point along subway line SLINE. As evidentfrom FIGS. 4 a through 4 e, and particularly in FIG. 4 d, side track 54w is positioned relative to main track 52 w in similar fashion as sidetrack 54 e is to its main track 52 e. FIG. 4 e illustrates the situationof FIG. 4 d, in which local trains LOC_(e), LOC_(w) are stopped on theirrespective side tracks 54 e, 54 w, in both directions at the sameexpress station E_(x). As evident from FIG. 4 a, side track 54 may beplaced either “uptrack” or “downtrack” from its associated platform 50;of course, as will become apparent from the following description, thescheduling and train car assignments generated for subway line SLINE bysystem 20 must take into account the position of side tracks 54 relativeto their express stations.

It is contemplated that the separation distance D_(sep) between adjacenttrains LOC, EXP on one of main tracks 52 and its corresponding sidetrack 54 can be significantly smaller than separation distance D_(trv)between passing trains on main tracks 52, 54 because the relative speedswith which adjacent trains LOC, EXP are traveling in the same directionat the locations of side tracks 54 are at best quite slow. When trainsLOC, EXP traveling in the same direction are adjacent to one another atthe location of side track 54, one of the two trains (typically localtrain LOC) is necessarily stopped, and the other train (typicallyexpress train EXP) is either stopping, starting, or completely stoppeditse1 f. On the other hand, passing trains on main tracks 52 e, 52 w maybe traveling at their full speeds when passing by one another, withtheir speeds relative to one another amounting to the sum of theirindividual instantaneous velocities (as they are passing in oppositedirections). Accordingly, it is contemplated that station separationdistance D_(sep) can be significantly smaller than passing separationdistance D_(trv), enabling passenger transfer directly from train totrain.

FIGS. 5 a through 5 e illustrate the operation of subway line SLINE inconnection with stops of express train EXP₀ and local train LOC₀ atexpress station E_(x) of the embodiment of the invention described aboverelative to FIGS. 4 a through 4 e. This description will assume thatpassengers on a given train (especially if the train is crowded) may notnecessarily move from car-to-car within that same train, as is typicalin modern subway trains. As described above, in this embodiment of theinvention, passenger transfer between express train EXP₀ and local trainLOC₀ occurs at a point beyond platform 50 e. FIG. 5 a illustrates afirst step in the overall process, with eastbound local train LOC₀making its stop at express station E_(x) along main track 52 e, andadjacent eastbound platform 50 e. Passengers board and de-board localtrain LOC₀ from and to platform 50 e, during the time period illustratedin FIG. 5 a.

After the stop made by local train LOC₀ at platform 50 e in FIG. 5 a,local train LOC₀ then proceeds onto side track 54 e, and waits on sidetrack 54 e, in order to enable a later-arriving express train EXP₀ topass at this express station E. This state of operation is illustratedin FIG. 4 b, along with express train EXP₀ approaching express stationE_(x) and its platform 50 e, on main track 52 e. FIG. 5 c illustratesthe position of express train EXP₀ as it stops at express station E_(x),specifically with express train front half EXP_(0,F) stopped adjacent tolocal train LOC₀, and express train rear half EXP_(0,R) stopped adjacentto platform 50 e; FIG. 5 c also illustrates that local train LOC₀ hasbacked up from its earlier position shown in FIG. 5 b, and now abuts theend of platform 50 e. As mentioned above, the doors of the cars ofexpress train front half EXP_(0,F) should be aligned with doors of thecars of local train LOC₀ at this stage of operation. Passenger transferbetween express train front half EXP_(0,F) and local train LOC₀, andbetween platform 50 e and express train rear half EXP_(0,R), then takesplace in the stage of operation illustrated in FIG. 5 c. Insofar asexpress train EXP₀ is concerned, the effective length of the platform,as established by the combination of platform 50 e and local train LOC₀,is twice that of platform 50 e itself.

It is useful at this point to consider the various passengers on boardtrains LOC₀, EXP₀ and other trains along subway line SLINE, with respectto their respective trips. Those passengers that board at a localstation, remain on a local train throughout their trip, and exit at alocal station will be referred to in this specification as “LLL”passengers (i.e., “local-local-local” passengers). Similarly, thosepassengers that board at an express station, remain on an express trainthroughout their trip, and exit at an express station will be referredto herein as “EEE” passengers (i.e., “express-express-express”passengers). In these embodiments of the invention in connection withside-by-side transfer, neither of the EEE or LLL passengers need make atransfer. Some passengers, however, will wish to take advantage ofexpress train service even though embarking or disembarking at alocal-only station. Those passengers who board at a local station,transfer at some point to an express train during their trip, andde-board at a local station, will be referred to herein as “LEL”passengers (i.e., “local-express-local” passengers). Other combinationsare also possible, such as those passengers who board at an expressstation, travel at least one interval on an express train, but exit at alocal station; these passengers will be referred to herein as “EEL”passengers (i.e., “express-express-local” passengers). “LEE” passengersof course board at a local station, transfer to an express train, andexit at an express station.

Referring again to FIG. 5 c, the EEE and LLL passengers will of courseremain on their respective trains EXP₀, LOC₀ during the stop andtransfer operation. Those LEL or EEL passengers currently on expresstrain EXP₀ and for whom express station E_(x) is the last expressstation along subway line SLINE before their local destination stationshould transfer from express train EXP₀ to local train LOC₀ while trainsEXP₀, LOC₀ are in the position of FIG. 5 c. Similarly, LEL and LEEpassengers currently on local train LOC₀ should transfer to expresstrain EXP₀ during the time that trains EXP₀, LOC₀ are in the position ofFIG. 5 c, and should remain on that until their destination expressstation (for LEE passengers) or until the last express station beforetheir destination local station (for LEL passengers). As evident fromthis description, every passenger can travel along subway line SLINEaccording to this embodiment of the invention without setting foot onany platform 50 other than at their ultimate starting and destinationstations.

Once passenger transfer is completed, then express train EXP₀ is allowedto leave express station E_(x) via main track 52 e, while local trainLOC₀ remains stopped on side track 54 e. This operation is illustratedin FIG. 5 d, which shows express train rear half EXP_(0,R) leavingexpress station E_(x) on main track 52 e (on which it has remainedthroughout the process of the stop at express station E_(x)). In thisway, later-arriving express train EXP₀ physically passes local trainLOC₀, which arrived at express station E_(x) before express train EXP₀but is leaving express station E_(x) later. After express train EXP₀ hasleft express station E_(x), then local train LOC₀ leaves express stationE_(x) by traveling from side track 54 e to main track 52 e, as shown inFIG. 5 e.

As evident from FIGS. 4 b, 4 c, and 5 c, simultaneous transfer ofpassengers between trains LOC₀, EXP₀ directly, and between express trainEXP₀ and platform 50 e is enabled by the use of an express train EXP₀with greater length than its corresponding local train LOC₀. In oneexample of the operation of subway line SLINE according to thisembodiment of the invention, for passenger safety, inter-car transferwithin the same train is not permitted, nor are passengers permitted totransfer between platform 50 e and local train car LOC₀(n) in thesituation shown in FIGS. 4 c and 5 c. As such, at express station E_(x)of FIGS. 4 a through 4 e and 5 a through 5 e, passengers boardingexpress train EXP₀ from platform 50 e (such passengers preferably of theEEE types in this embodiment of the invention) can only board cars inexpress train rear half EXP_(0,R); meanwhile, passengers transferringbetween express train EXP₀ local train LOC₀, in either direction, canonly do so relative to express train front half EXP_(0,F). As such, onlythose passengers riding in express train front half EXP_(0,F) cantransfer to local train LOC₀ (and thus de-board at one of the upcominglocal stops) over the express interval I_(x) beginning with expressstation E. Passengers riding in express train rear half EXP_(0,R) mustremain on express train EXP₀ until at least the next express stationE_(x+1) in this example. Passengers boarding at express station E_(x)but whose destination is a local station (i.e., EEL passengers) shouldboard local train LOC₀ when it arrives at platform 50 e (FIG. 5 a) andthen transfer to express train EXP₀ during a side-by-side transfer asshown in FIG. 5 c.

It is contemplated that the schedule generated by system 20 for localand express trains along subway line SLINE will in some way comprehendthis limitation relative to the boarding and de-boarding of expresstrains EXP₀, and transfers to and from local trains LOC. Of course,express trains EXP stopping at express station E_(x) may make two shortstops: one stop with express train front half EXP_(0,F) at platform 50e, and the second stop with express train rear half EXP_(0,R) atplatform 50 e (indeed, one can contemplate a third stop, with expresstrain rear half EXP_(0,R) adjacent local train LOC₀). However, it iscontemplated that such multiple stops by express trains at each expressstation will add to the overall passenger travel time for both expressand local passengers (especially considering that this additional timewill occur at every express station), and is therefore disfavored.

Referring now to FIGS. 5 f and 5 g, the operation of this embodiment ofthe invention in connection with express train EXP₀ of the same lengthof local train LOC₀, and thus of about the same length as platform 50 eat which it is making a stop, will now be described. In FIG. 5 f, localtrain LOC₀ is positioned on side track 54 e; prior to the point in timeshown in FIG. 5 f, local train LOC₀ had already stopped at platform 50 eto allow passengers to board and de-board, following which it proceededdown main track 52 e and then backed into side track 54 e. At the pointin time shown in FIG. 5 f, express train EXP₀ has arrived at expressstation E_(x), and is aligned with platform 50 e to permit passengers toboard and de-board (e.g., EEE and LEE passengers).

The approach shown in FIG. 5 f provides the ability for express trainEXP₀ to physically pass earlier arriving local train LOC₀ at an expressstation E_(x) that has a reduced footprint. However, the passing processin that embodiment of the invention requires express train EXP₀ to maketwo full stops—one at platform 50 e to permit passengers to board anddeboard express train EXP₀ from and to express station E_(x), andanother stop adjacent to local train LOC₀ to permit EEL passengers totransfer from express train EXP₀ to local train LOC₀. According to analternative approach shown in FIG. 5 g, express train EXP₀ canaccomplish the necessary passenger movements in a single stop. At thepoint in time shown in FIG. 5 g, express train EXP₀ makes its stop atexpress station E_(x) at a position that is half-aligned with platform50 e and half-aligned with local train LOC₀. This stop position allowspassengers to board and deboard the rear half of express train EXP₀ fromand to express station E_(x), and simultaneously allows directtrain-to-train passenger transfers between trains LOC₀ and EXP₀. Morespecifically, EEE passengers will board the rear half of express trainEXP₀. LEE passengers, who previously de-boarded local train LOC₀ at itsstop at platform 50 e, will also board the rear half of express trainEXP₀; these LEE passengers will have been instructed or restricted tohave boarded the front half of local train LOC₀ at their station oforigin, and will have been instructed to de-board local train LOC₀ atplatform 50 e. Those LEL passengers who are transferring to expresstrain EXP₀ for the express portion of their journey over the nextexpress interval will have been instructed to have boarded the rear halfof local train LOC₀ at their station of origin, so that they can makethe direct transfer to the front half of express train EXP₀ at thistime. Therefore, at the point in time shown in FIG. 5 g, these LELpassengers on the rear half of local train LOC₀ can transfer directly tothe front half of express train EXP₀ to begin the express portion oftheir journey, and LEL and EEL passengers already on the front half ofexpress train EXP₀ can transfer directly to the rear half of local trainLOC₀ to begin the final local portion of their journey. Following thisdirect transfer opportunity, express train EXP₀ leaves express stationE_(x) first, followed by local train LOC₀, as described above relativeto FIGS. 5 d and 5 e.

According to another embodiment of the invention, side track 56 e islocated on the “uptrack” side of platform 50 e, to facilitate passengermovement as will now be described relative to FIGS. 5 h and 5 i for thecase of express train EXP₀ of the same length as local train LOC₀, andof a length that is about that of platform 50 e. As shown in FIG. 5 h,express station E_(x) has eastbound platform 50 e and westbound platform50 w associated with eastbound and westbound main track 52 e, 52 w,respectively. Platforms 50 e, 50 w are each associated with acorresponding uptrack side track 56 e, 56 w. Side tracks 56 e, 56 w areuptrack in the sense that it can receive a train prior to that trainarriving at the corresponding platform 50 e, 50 w.

FIG. 5 h illustrates the operation of express station E_(x) in servingstops for local train LOC₀ and express train EXP₀ in this embodiment ofthe invention. At the point in time shown in FIG. 5 h, local train LOC₀has already arrived at express station E_(x) from the west, but ratherthan stopping at platform 50 e, has pulled into uptrack side track 56 e.Express train EXP₀ has arrived at station E_(x) later than did localtrain LOC₀, and is shown in FIG. 5 h in its positioned as stopped atplatform 50 e. In this embodiment of the invention, express train EXP₀stops with its leading portion at platform 50 e, and its trailingportion aligned with the leading portion of local train LOC₀. In thisposition, boarding express passengers (i.e., both EEE and EELpassengers) may board express train EXP₀ from the rear half of platform50 e, and de-boarding express passengers (i.e., both EEE and LEEpassengers) may de-board express train EXP₀ to platform 50 e. Meanwhile,passengers (e.g., EEL, LEL passengers) may transfer directly from therear half of express train EXP₀ to local train LOC₀, and passengers(e.g., LEL, LEE passengers) may transfer directly from the front half oflocal train LOC₀ to express train EXP₀, in the manner described aboverelative to FIG. 4 d. Following this stop, express train EXP₀ may thendirectly leave platform 50 e and express station E_(x) via main track 52e, continuing its express service along subway line SLINE, as shown inFIG. 5 i. In FIG. 5 i, local train LOC₀ has moved forward, via spur 56′,to stop at platform 50 e. At this time, LEE passengers who previouslytransferred to local train LOC₀ from the rear half of express train EXP₀(FIG. 5 h) may then de-board local train LOC₀ to platform 50 e. EELpassengers who previously de-boarded from the front half of expresstrain EXP₀ may then re-board local train LOC₀ for the local leg of theirjourney to the desired local destination station along the nextinterval.

In this embodiment of the invention, the efficiency of the stop atexpress station E_(x) for local train LOC₀ is improved relative to thatdescribed above in connection with FIGS. 4 a through 4 d, because localtrain LOC₀ need not back up over more than its entire length in order toutilize side track 56 e; rather, local train LOC₀ need only back up ashort distance away from platform 50 e along side track 56 e, beforemoving forward again via spur 56′ to main track 52 e and platform 50 e.The efficiency of the stop for express train EXP₀ is also improved,because express train EXP₀ need only make one stop rather than two.Those passengers in the rear half of express train EXP₀ can de-board atplatform 50 e by first transferring to local train LOC₀ (FIG. 5 h), andthen de-boarding local train LOC₀ when it stops at platform 50 e (FIG. 5i). Passengers who wish to transfer from the front part of express trainEXP₀ may also perform a two-step transfer, from express train EXP₀ toplatform 50 e and then from platform 50 e to local train LOC₀.

In summary, the operation of express station E_(x) shown in FIGS. 5 hand 5 i is less restrictive than that shown in FIG. 5 g. Morespecifically, the entire length of express train EXP₀ has access, eitherdirect or indirect, to platform 50 e and the entire length of localtrain LOC₀; the front half of local train LOC₀ also has access to bothplatform 50 e and express train EXP₀. Passengers already in the rearhalf of local train LOC₀ are still partially restricted, in that theycannot transfer to express train EXP₀; it is contemplated, however, thatpassengers can be instructed by system 20, at their station of origin,to board the front half of local train LOC₀ if they intend to transferan express train. The rear half of local train LOC₀ can receive EEL andLEL passengers from express train EXP₀ indirectly, at its stop atplatform 50 e at the point in time shown in FIG. 5 i.

FIGS. 5 j and 5 k illustrate the operation of the eastbound side ofexpress station E_(x) with uptrack side track 56 e in the case in whichexpress train EXP₀ is of twice the length of local train LOC₀ and ofplatform 50 e. In the state of operation shown in FIG. 5 j, local trainLOC₀ has already arrived at express station E_(x), and has pulled intoside track 56 e before stopping at platform 50 e. Later, express trainEXP₀ has arrived at express station E_(x), and is stopped with its fronthalf EXP_(0,F) at platform 50 e and its rear half EXP_(0,R) aligned withlocal train LOC₀. Passengers may board and de-board express train fronthalf EXP_(0,F) from and to platform 50 e at this time, and passengersmay transfer directly between local train LOC₀ and express train rearhalf EXP_(0,R) in the manner described above relative to FIG. 4 d.Express train EXP₀ can then leave express station E_(x) after thissingle stop.

In FIG. 5 k, express train EXP₀ has left express station E_(x), andlocal train LOC₀ has backed up slightly, and then moved forward via spur56′ to stop at platform 50 e. As before, passengers may now board localtrain LOC₀ from platform 50 e, and other passengers may de-board localtrain LOC₀ to platform 50 e (including those passengers who transferredto local train LOC₀ from express train rear half EXP_(0,R) during thestop shown in FIG. 5 j). As a result, each of local train LOC₀ andexpress train EXP₀ need make only a single stop at express stationE_(x), while permitting full flexibility in the movement of passengersbetween trains LOC₀, EXP₀.

This operation of subway line SLINE according to these embodiments ofthis invention can be further described in connection with the schematicviews of subway line SLINE shown in FIGS. 5 l through 5 o. Similarly asin the case of FIGS. 3 e through 3 h, FIGS. 5 l through 5 o are planviews of subway line SLINE from above (and through the earth abovesubway line SLINE) at particular points in time. FIG. 5 l illustratesthe state of subway line SLINE at a point in time in which express train{circumflex over (T)}6 is beginning the trip along subway line SLINE, atexpress station E0, just ahead of local train T12; meanwhile, at thispoint, express trains {circumflex over (T)}5, {circumflex over (T)}4,and {circumflex over (T)}3 have caught up to their respective localtrains T10, T8, T6 at express stations E1, E2, E3, respectively. Assuch, according to embodiments of this invention described above inconnection with FIGS. 4 a through 4 d and 5 a through 5 i, expresstrains {circumflex over (T)}5, {circumflex over (T)}4, and {circumflexover (T)}3 physically pass their respective local trains T10, T8, T6;FIG. 5 m illustrates subway line SLINE at this point in time after thisphysical passing operation. As described above, these physical passoperations also involve passenger boarding, de-boarding, and transfer.FIG. 5 n illustrates the state of subway line SLINE at a time during thenext express interval, in which express trains {circumflex over (T)}6,{circumflex over (T)}5, {circumflex over (T)}4, and {circumflex over(T)}3 are traveling along subway line SLINE ahead of the local trainsT12, T10, T8, T6 that they recently passed. However, each of theseexpress trains {circumflex over (T)}6, {circumflex over (T)}5,{circumflex over (T)}4, and {circumflex over (T)}3 are catching up tothe local trains T11, T9, T7 etc. that are ahead along subway lineSLINE, as shown in FIG. 5 n. And, as shown in FIG. 5 o, express trains{circumflex over (T)}6, {circumflex over (T)}5, and {circumflex over(T)}4, catch up to respective local trains T11, T9, T7, at the nextexpress station E1, E2, E3, respectively. At that time, as shown in FIG.5 o, the next express train {circumflex over (T)}7 is sent along subwayline SLINE from origin station E0, ahead of the next local train T13. Ofcourse, in the same manner as shown in FIG. 5 m, express trains{circumflex over (T)}6, {circumflex over (T)}5, and {circumflex over(T)}4 will physically pass these respective local trains T11, T9, and T7in the manner described above, in connection with FIGS. 4 a through 4 dand 5 a through 5 i, continuing the process.

According to each of these embodiments of the invention, therefore,express train EXP₀ can physically pass local train LOC₀ at expressstation E_(x), thus enabling express service over a single track onwhich local trains also operate. While flexibility in passenger movementis provided by these embodiments of the invention, it is useful forsystem 20 to assist passengers by way of at-station and on-traingraphics displays instructing passengers regarding the portion of thetrain that they ought to board in order to carry out their desiredtransfers to and from express trains, for example in order to optimizetravel to a particular destination station. It may be useful that suchat-station and on-train displays illustrate visualizations of theentirety of subway line SLINE to show the approach and passing of localtrains by express trains, to assist passenger understanding of thisoperation. Alternatively, or in addition, system 20 may also providetransfer and car assignment instructions in connection withpoint-to-point ticketing.

As evident in each of these embodiments of the invention, expressstation E_(x) is no wider (i.e., in the direction perpendicular totracks 52) due to the presence of side tracks 54 e or 56 e, than thatwhich is otherwise necessary to provide main tracks 52 e, 52 w andplatforms 50 e, 50 w without side tracks. Accordingly, existing subwaylines may be retrofitted by construction of side tracks 54 at itsexpress stations, with much reduced excavation and construction coststhan would be required to include conventional side tracks on oppositesides of the platform (as described above relative to FIG. 1). It istherefore contemplated that, in many existing subway systems, theprovision of express subway service over two-track subway lines isrendered feasible by this embodiment of the invention.

Local to Express Train “Transformation”

According to another embodiment of this invention, express and localsubway trains traveling along the same two-track subway line SLINE arescheduled and operated to meet at express stations only, similarly as inthe embodiments described above in which express trains physically passthe earlier-arriving local trains. According to this embodiment of theinvention, however, express trains can be considered to “virtually” passthe local trains. This is accomplished by transforming individual trainsfrom providing express service to providing local service, and viceversa, at express stations. In other words, the same physical train thatprovides local service over one interval between express stations istransformed to provide express service over the next interval betweenexpress stations; conversely, the same physical train that providesexpress service over one interval between express stations may betransformed to provide local service over the next interval betweenexpress stations.

In a general sense, according to this embodiment of the invention, agroup of n trains (n≧2) traveling in the same direction arrivesimultaneously at an express station along the two-track subway lineSLINE. In this case, the earliest arriving train (or trains) will havebeen providing local service over the previous interval between expressstations, and later arriving trains will have been providing expressservice over that interval, catching up to the local train at theexpress station according to the schedule. According to this embodimentof the invention, the last one or more of the express trains arriving atthis express station (which, given the above description, mean the lastone or more of the trains in this group of trains) provide local serviceover the next interval between express stations. The earliest arrivingtrain (formerly providing local service) and perhaps one or more of thenext-to-arrive trains at this express station provide express serviceover the next interval between express stations. Because of thistransformation, the train that is providing local service is no longerat the head of the group of trains, but is at the tail—this localservice train will not hold up the progress of the express trains thatare now in front of it along subway line SLINE.

FIG. 6 illustrates this scheduling and operation of trains according tothis embodiment of the invention, by way of a travel diagram. In thisexample, three trains TRN₁, TRN₂, TRN₃ are traveling in the samedirection along a two-track subway line SLINE, and are traveling fromexpress station E0 to express station E3. It is contemplated that thisoperation of subway line SLINE in a manner according to this embodimentof the invention may be based on a schedule created by a computersystem, such as system 20 described above relative to FIG. 3 a, forexample as generated and modified by way of the process described aboverelative to FIG. 3 b. In addition, it is contemplated that system 20 canalso monitor the real-time operation of trains along subway line SLINE,and control or suggest the operation of trains (e.g., by way ofinstantaneous travel velocity, or delays at particular stations, and thelike) to minimized wait times and other non-productive delays. Asdescribed above, the scheduling of trains TRN₁ et seq. is performed witha goal of express trains catching up to local trains only at expressstations, thus minimizing the time and distance over which the travelvelocity of a subway train providing express service is limited by alocal subway train traveling ahead of it along the same track.

As evident from FIG. 6, according to this embodiment of the invention,express trains travel at an effective travel velocity V_(exp); at thatexpress velocity V_(exp), a train may travel from one express station tothe next (e.g., from station E0 to station E1) within one time interval(time t1 to time t2). Local trains travel at an effective travelvelocity V_(loc), which in the example of FIG. 6 is one-half of expressvelocity V_(exp). As such, a train traveling at local velocity V_(loc)requires two time intervals (e.g., time t0 to time t2) to travel fromone express station to the next (station E0 to station E1). As discussedabove, the slower effective travel velocity V_(loc) for trains providinglocal subway service need not necessarily result from a slowerinstantaneous velocity, but may instead result from the intermediatestops made at local stations along the interval between expressstations.

In the example of FIG. 6, and according to this embodiment of theinvention, train TRN₁ leaves express station E0 at time t1. Train TRN₁provides local service over the interval between express stations E0 andE1, travelling at local travel velocity V_(loc), until reaching expressstation E1 at time t3. Train TRN₂ leaves express station E0 at a latertime t2, but travels at express travel velocity V_(exp) so that it alsoarrives at express station E1 at time t3. However, because train TRN₁left station E0 immediately before train TRN₂, train TRN₁ occupies aposition on two-track subway line SLINE ahead of train TRN₂, and thusarrives at express station E1 ahead of (but essentially simultaneouslywith) train TRN₂. According to this embodiment of the invention, trainTRN₁ “transforms” into an express train at express station E1, and assuch travels at express velocity V_(exp) over the interval betweenexpress stations E1 and E2. Conversely, train TRN₂ transforms into alocal train at express station E1 to provide local service over theinterval between express stations E1 and E2, travelling at localvelocity V_(loc). Because local velocity V_(loc) is slower than expressvelocity V_(exp), train TRN₂ falls behind train TRN₁ over this interval;conversely, train TRN₁ is not held up by a slower-moving local trainahead of it on the track (at least until reaching express station E2 attime t4, at which time it catches up to a local train, if any, that isahead of it on the track).

Meanwhile, train TRN₃ leaves express station E0 at time t2, at whichpoint it provides local service over the interval between stations E0and E1. In doing so, train TRN₃ travels at the slower local effectivetravel velocity V_(loc), arriving at express station E1 at time t4, onetime interval after train TRN₂ arrived at express station E1. Over thenext interval, between stations E1 and E2, train TRN₃ transforms into anexpress train, traveling at express travel velocity V_(exp), andarriving at express station E2 at time t5. Meanwhile, train TRN₂ hasprovided local service, at effective local travel velocity V_(loc),between express stations E1 and E2, reaching the next express station E2at time t5. Because train TRN₂ is ahead of train TRN₃ on the track,train TRN₃ essentially catches up to train TRN₂ at express station E2,but cannot physically pass train TRN₂. Instead, according to thisembodiment of the invention, train TRN₂ transforms into an express trainat station E2, traveling at express travel velocity V_(exp) over theinterval between express stations E2 and E3; train TRN₃ transforms intoa local train at station E2, providing local service over the intervalbetween express stations E2 and E3 and traveling at local travelvelocity V_(loc).

The operation of trains TRN₁, TRN₂, TRN₃ continues in this manner, alongwith those trains ahead of and following after these trains along subwayline SLINE. In this example, each train traveling along two-track subwayline SLINE alternates between providing local service and providingexpress service, from express interval to express interval. In effect,therefore, each train operates at a higher average travel velocity overthe entire length of subway line SLINE, considering that each train doesnot make local stops over alternating express intervals (and may alsotravel at higher instantaneous velocities over those intervals,depending on the schedule and operator). The schedule generated andoperated by the subway operator, for example through the use of system20 and the process of FIG. 3 b, optimizes efficiency of this operationby limiting the time that the faster moving express trains are held upby the slower traveling local trains.

In the example of FIG. 6, trains TRN₁ through TRN₃ are effectivelytransforming at each express station as a group of two—each train andthe train immediately ahead of it or behind it at the express station,as the case may be. FIG. 7 a illustrates this operation of two-traingroups in further detail, relative to four trains T1 through T4proceeding in sequence in the same direction along two-track subway lineSLINE. In the example of FIG. 7 a, stop times at the various stationsare ignored, for clarity of the description.

As shown in FIG. 7 a, trains T2 and T3 arrive at and leave expressstation E0 at time t=10 minutes, with train T2 providing express servicefrom express station E0 and train T3 providing local service fromexpress station E0. In this example, train T2 in its express modearrives at express station E1 at time t=15 minutes, while at that sametime, train T3 arrives at local station L1 between express stations E0and E1. Meanwhile, train T1 has been providing local service betweenexpress stations E0 and E1, leaving express station E0 at time t=5minutes, stopping at local station L1 at time t=10 minutes, and arrivingat express station E1 just ahead of train T2 at time t=15 minutes. Assuch, at time t=15 minutes, both of trains T1 and T2 are at expressstation E1, with train T1 ahead of train T3 along two-track subway lineSLINE.

According to this embodiment of the invention, at express station E1 attime t=15 minutes, train T1 transforms from a local train into anexpress strain and train T2 transforms from an express train into alocal train. As such, train T1 provides express service from expressstation E1, arriving at express station E2 at time t=20 minutes, andtrain T2 provides local service from express station E1, arriving atlocal station L2 at time t=20 minutes. Meanwhile, train T3 arrives atexpress station E1 at time t=20 minutes, having provided local servicebetween express stations E0 and E1, immediately followed by train T4which has been providing express service between express stations E0 andE1. Train T3 transforms into providing express service from expressstation E1, beginning at time t=20 minutes, and arrives at expressstation E2 at time t=25 minutes, immediately after train T2, whichcontinued its local service from local station L2 until reaching expressstation E2 at that same time, but ahead of train T3. From this pointforward, the sequence of operations essentially repeats (i.e., thestatus of trains T1, T2, T3 at time t=25 minutes matches that at timet=10 minutes).

This process of alternating between providing express service andproviding local services continues over time, along two-track subwayline SLINE, in this two-train group example. Each train alternatesbetween providing express and local service in this manner, meeting upwith the trains immediately ahead and behind at each express station, inthe manner described above. As a result, each train travels at thehigher effective express velocity (V_(exp)) for half of the expressintervals, and at the slower effective local velocity (V_(loc)) for theother half of the express intervals. If the express intervals are ofequal length, and if local velocity V_(loc) is one-half that of expressvelocity V_(exp), then operation according to this two-train groupapproach provides a 25% reduction in the passenger travel time oversubway line SLINE.

According to this embodiment of the invention, trains may transformaccording to more than two trains per “group”. FIG. 7 b illustrates theoperation of subway line SLINE for the example of three-train groups, inwhich the last train in a given group leaving an express stationprovides local service over the express interval and the first twotrains provide express service over that interval. For example, threetrains T5, T6, T7 leave express station E0 at time t=15 minutes, in FIG.7 b. Train T7 provides local service from express station E0, arrivingat local station L1 at time t=20 minutes; meanwhile, trains T5 and T6provide express service from express station E0, arriving at expressstation E1 at time t=20 minutes. At that time t=20 minutes and atexpress station E1, trains T5 and T6 catch up to train T4, but remainbehind train T4 along subway line SLINE. Over the express interval fromexpress station E1, trains T4 and T5 provide express service, whiletrailing train T6 provides local service from express station E1,stopping at local station L2 at time t=25 minutes. Trains T4 and T5arrive at the next express station E2 at time t=25 minutes.

Train T7, which provided local service from express station E0, arrivesat express station E1 at time t=25 minutes. Trains T8 and T9, whichprovided express service from express station E0, also arrive at expressstation E1 at that time, but remain behind train T7 on subway lineSLINE. From express station E1, trains T7 and T8 provide expressservice, while trailing train T9 provides local service, stopping atlocal station L2 at time t=30 minutes, which in this example is the sametime that trains T7 and T8 arrive at express station E2. Train T6, whichprovided local service from express station E1, also arrives at expressstation E2 at time t=30 minutes, at which time it transforms intoproviding express service along with train T7; train T8 provides localservice from express station E2. The process continues in this manner,as shown in FIG. 7 b for these three-train groups, with trains T5, T6,T7 finally catching up to one another, as a group, at express station E3at time t=35 minutes, from which point the process repeats in the samemanner.

In this example, each train travels at the effective express travelvelocity V_(exp) for two out of every three express intervals, andtravels at the effective local travel velocity V_(loc) over the third ofthose intervals. Under the assumptions of express intervals of equallength, and local velocity V_(loc) one-half that of express velocityV_(exp), then operation according to this three-train group approachprovides a 33% reduction in the passenger travel time over the length ofsubway line SLINE.

FIG. 7 c illustrates the operation of subway line SLINE for the examplein which the trains meet at express stations in groups of four, with thetrailing train of that group providing local service over the nextinterval from express station. In this example, we will follow the groupof four trains T6, T7, T8, T9, which leave express station E0 at timet=15 minutes. The trailing train T9 in this group provides local serviceover the interval from express station E0, stopping at local station L1at time t=20 minutes, while trains T6, T7, T8 provide express serviceover that interval, arriving at express station E1 at time t=20 minutes.Train T5, having provided local service from express station E0, hasarrived at express station E1 immediately prior to trains T6, T7, T8, attime t=20 minutes. As such, from the group of trains T5, T6, T7, T8 atexpress station E1 at time t=20 minutes, train T8 is the rear-most trainof the group and thus will provide local service over the interval fromexpress station E1, arriving at local station L2 at time t=25 minutes.Trains T5, T6, T7 all provide express service over this interval,arriving at express station E2 at time t=25 minutes, immediately aftertrain T4. Meanwhile, train T9 continues at its local velocity, andarrives at express station E1 at time t=25 minutes.

This operation of trains T6, T7, T8, T9 and the other trains travelingalong subway line SLINE at this time continues in this fashion. Fromtime t=25, train T8 continues to provide local service and train T7begins providing local service (from express station E2); meanwhile,trains T6 and T9 provide express service over their respectiveintervals. Eventually, at time t=40 minutes, the original group of fourtrains T6, T7, T8, T9 that we followed above from express station E0arrive together again at express station E4, at time t=40 minutes, fromwhich point the process repeats again, continuing over the length ofsubway line SLINE.

In this example, one train in every group of four trains is providinglocal service over an interval between express stations, while the otherthree trains are providing express service. With respect to a singletrain, each train operates at effective local travel velocity V_(loc)over every fourth interval between express stations, and operates at theeffective express travel velocity V_(exp) over the other three intervalsin that group of intervals. Under the assumptions of express intervalsof equal length, and local velocity V_(loc) one-half that of expressvelocity V_(exp), then operation according to this three-train groupapproach provides nearly a 40% reduction in the passenger travel timeover the length of subway line SLINE.

In particular, it can be appreciated that the density of trains per unitdistance along subway line SLINE can greatly decrease, for a givenpassenger throughput rate, through use of embodiments of this invention.FIGS. 7 d through 7 g illustrate this effect, in the form of satellite“snapshots” of the status of subway line SLINE at various points intime. The snapshots of FIGS. 7 d through 7 f illustrate the status ofsubway line SLINE at the same point in time (i.e., that point in time atwhich train T0 has reached express station E6) relative to one another,but for different train densities along subway line SLINE, as will nowbe described.

FIG. 7 d illustrates a portion of subway line SLINE between expressstations E0 and E6 in its conventional operation, in which every trainoperates as a local train. The distance intervals between the variousexpress stations E0 through E6 are shown as uniform, for the sake ofclarity; as discussed above, of course, this uniform interval is not arequirement in embodiments of this invention. In the case shown in FIG.7 d, trains T0 through T12 operate in single train “groups”; each trainT0 through T12 is providing only local service. Trains T0 through T12are spaced in time from one another, and all of trains T0 through T12operate at the same average travel velocity as one another. Whileexpress stations E0 through E6 are shown in FIG. 7 d, those stations arefunctionally indistinct from one another and from any other stationalong subway line SLINE, as there is no express service and thus eachstation serves as a local station. In the case shown in FIG. 7 d, thedensity of trains per unit express interval is two.

FIG. 7 e shows subway line SLINE at a similar instant in time as that ofFIG. 7 d, but shows the case in which each train alternates betweenproviding express service and local service. This corresponds to thetwo-train groups described above relative to FIG. 7 a. In FIG. 7 e,those trains indicated with the “̂” character (i.e., trains T1, T4, T7,T10, T13, T16, T19) are currently providing express service, and areshown in the order as arriving at the various express stations E0through E6 (i.e., before making a physical or virtual pass of theircorresponding local train also at that station). For example, at expressstation E1 in FIG. 7 e, train T15 is the first to arrive and has beenproviding local service over the previous interval; train T16 will benext to arrive, and has been providing express service over the previousinterval; as described above, train T15 will then provide expressservice over the next interval, and train T16 will provide local serviceover that next interval. Because one out of every three trains on agiven express interval of subway line SLINE is providing expressservice, at essentially twice the average travel velocity along thelength of subway line SLINE, three trains are capable of providing thesame passenger throughput according to this invention that would requirefour local-only trains in the conventional local-only subway system asshown in FIG. 7 d. Not only do embodiments of this invention thusprovide greater efficiency in train and fuel utilization than does thelocal-only service, but as many as one-half of the passengers (on theaverage) will experience a significantly shorter travel time. In thecase shown in FIG. 7 e, the density of trains per express interval isthree (rather than two in the case of FIG. 7 d). But the passengerthroughput capacity of the case of FIG. 7 e is twice that of the case ofFIG. 7 d, and indeed is equivalent to the throughput capacity of adensity of four local-only trains.

As described above, the subway operator can increase the density oftrains to take further advantage of the improvement in efficiency,assuming that additional passenger demand is available. The snapshot ofsubway line SLINE shown in FIG. 7 f illustrates the three-train groupoperation described above relative to FIG. 7 b, in which two trains ofevery four are providing express service over any given express intervalof subway line SLINE. In the case shown in FIG. 7 f, the density oftrains per express interval is four. Because these express trains aretraveling at twice the average travel velocity as the local trains, thearrangement of FIG. 7 f is capable of carrying the same passengerthroughput that would require six local-only trains in the conventionallocal-only subway system of FIG. 7 d. If supported by the passengerdemand, FIG. 7 g illustrates the case in which three of every fivetrains are providing express service over each express interval ofsubway line SLINE, as described above relative to FIG. 7 c in connectionwith the four train groups. In the case of FIG. 7 g, the density oftrains per express interval is five, and those five trains are capableof supporting the same passenger throughput that would require eightlocal-only trains in the conventional local-only subway system of FIG. 7d. Again, not only is the train and fuel utilization improved throughuse of embodiments of this invention, but increasing fractions ofpassengers will experience shorter travel times. In some embodiments ofthis invention, as will be described below, this shorter travel time ismade available to essentially every passenger.

Table 1 tabulates, for the trains in a given group, the intervals overwhich each train is providing express service and over which each trainprovides local service:

TABLE 1 # of Train position Express Express Express Express ExpressExpress trains per when leaving interval 1 interval 2 interval 3interval 4 interval 5 interval 6 FIG. group E0 (E0 to E1) (E1 to E2) (E2to E3) (E3 to E4) (E4 to E5) (E5 to E6) 7d 1 Head L L L L L L 7e 2 HeadE L E L E L Tail L E L E L E 7f 3 Head E E L E E L Middle E L E E L ETail L E E L E E 7g 4 Head E E E L E E Mid 1 E E L E E E Mid 2 E L E E EL Tail L E E E L EThis Table 1 presumes that only one of the trains in a given group oftrains provides local service, allowing the other trains in that groupto operate at the faster effective express velocity V_(exp). In eachcase, the last train in any group to leave any express station willprovide local service over the next express interval; conversely, thefirst train to leave any express station will provide express serviceover the next express interval. In those cases in which the number oftrains within a group is greater than two, optimum express service isattained by all trains in the group, except the last to leave theexpress station, providing local service over the next interval.

In each of the cases of FIGS. 7 a through 7 c described above, the trainproviding local service within an express interval serves as the“pacemaker” for all of the express trains following it within theinterval. The travel time of this local train (e.g., train T14 betweenexpress stations E1 and E2 in FIG. 7 e) is entirely independent of thenumber of express trains following it over that interval. As such, theschedule of local service over the entirety of subway line SLINE canremain constant, regardless of the density of trains on that line. Thisremarkable result enables the subway operator to vary the number ofexpress trains serving subway line SLINE over time, for example withinthe same day (rush hour vs. non-rush hour), from day to day (weekdaysvs. weekends), or for special events (sporting events, festivals, etc.),without changing the schedule of the local train service. This abilityis contemplated to greatly facilitate passengers in arranging theirtravel, because the frequency and schedule of subway train service canremain completely fixed, regardless of time of day and day of the week.The consumer can arrange travel with confidence and ease, by relying onthe local train schedule as a minimum; upon arrival at the trainstation, in-station graphics displays or station-to-station ticketingcan advise the passenger of the availability of any express service atthat time. Indeed, it is contemplated that this consistency in trainscheduling will not only improve customer convenience, but as a resultwill increase ridership during off-peak times.

While the improvement in average train travel velocity increases as thenumber of trains per group increases, because a higher fraction of thetrains are traveling at the faster express velocity V_(exp) than at theslower local velocity V_(loc), the effective passenger travel time willdecrease only if there are a sufficient number of passengers using theexpress service to support the number of express trains assigned.Accordingly, the selection of the number of trains assigned to eachgroup depends on the relative passenger demand for express vs. localservice. It is contemplated that system 20 of FIG. 3 a, operatingaccording to the process illustrated in FIG. 3 b and described above,will be capable of deriving the optimum schedule considering thesefactors of travel time and passenger demand, and other factorsapplicable to subway line SLINE including the available trains, theeffects of stop times at each of the stations, any extraordinary eventsoccurring along the line that affect operation, and the like. Of course,subway system management may also have certain operational constraintsthat also affect the derivation of the schedule, which must also betaken into account as appropriate. In any event, it is contemplated thatthe operator of subway line SLINE is able to adjust for the varyingvolume of passengers at different times of day, and on different days,by adjusting the number of express trains assigned. For example, duringrush hour, a larger number of express trains can be used (e.g., as shownin FIGS. 7 f and 7 g), while at non-rush hour times or holidays andweekends, fewer trains may be assigned as express trains (e.g., as shownin FIG. 7 e or, in the extreme case, providing local service only asshown in FIG. 7 d). In this way, local and express service can remainavailable for every customer, with local service following the scheduleduring non-peak times as during peak usage times, while system 20 isprovided with the ability to respond to peak rush hour usage withoutnecessarily altering the schedule.

FIGS. 8 a through 8 c illustrate an optimum sequence by way of whichtrains may arrive at and depart an express station according to thisembodiment of the invention. As evident from the foregoing description,train wait times constitute an important factor in the overall traveltime of each passenger along subway line SLINE. According to thisembodiment of the invention, in which a first train of a group arrivingat an express station at the same time is transforming from localservice to express service (such a train referred to herein as an “LE”train) while the last train in the same group of trains arriving at thatexpress station is transforming from express service to local service(such a train referred to herein as an EL train), the later-arrivingtrains in the group can be forced to wait for the first train (the LEtrain) to leave the platform. Any time that elapses while the second andremaining trains are stopped at an express station short of the platformand waiting for the first train to leave is not only wasted travel timethat lengthens the time of the overall trip, but is also annoyinglynoticeable to the passengers on the stopped train. It is thereforebeneficial to minimize such waiting time at the express stations.

FIGS. 8 a through 8 c illustrate the operation of a three-train group,similar to that described above relative to FIG. 7 b, in stopping atplatform 50 of an express station. At the point in time shown in FIG. 8a, train T60 is stopped at platform 50, with passengers boarding andde-boarding train T60 at that time. Train T60 is an LE train, in that ithad provided local service over the express interval leading up toplatform 50, but will provide express service over the next interval.Train T62 is the next train to arrive at platform 50, and has beenproviding express service over the preceding express interval. At thepoint in time shown in FIG. 8 a, train T62 is still moving towardplatform 50, but has not yet arrived. Similarly, train T64 is the lasttrain in this three-train group, and trails train T62 by some distance;train T64 is an EL train at this point in time, as it is currentlyproviding express service over the express interval preceding platform50 but will provide local service over the interval following platform50.

FIG. 8 b illustrates a point in time later than that shown in FIG. 8 a,at which train T60 has already left platform 50 and is proceeding alongthe next express interval, and will be providing express service. TrainT62 is now at platform 50, with passengers boarding and de-boardingtrain T62 during this time. Train T64 is still some distance away fromplatform 50. Again, both of trains T60, T64 are moving during the timethat train T62 is stopped at platform 50. FIG. 8 c depicts a later pointin time than that of FIG. 8 b, at which time train T62 has now also leftplatform 50 and at which train T64 is stopped at platform 50. Passengerswho wish to stop at a local station along the next express interval fromplatform 50 will be boarding train T64 at this time, and passengers ontrain T64 who are terminating their trip at this station will bede-boarding.

It is contemplated that system 20 can schedule and manage the velocitiesof trains T60, T62, T64 to optimize the efficiency of the stop of eachtrain at platform 50. As such, the particular distances between trainsT60, T62, T64 in this example shown in FIGS. 8 a through 8 c can vary.However, it is contemplated that system 20 can optimize these spacingdistances in a manner that minimizes the time that each train T60, T62,T64 is stopped at or before platform 50, and that also minimizes thetime between the departure of one train and the arrival of the next. Inother words, the scheduling and operation of trains T60, T62, T64 can bemanaged by system 20 to minimize the wait times for those passengerstransferring from one of trains T60, T62 to train T64, while alsoeliminating any time that a later train is stopped short of platform 50,waiting for a train currently at platform 50 to leave.

If the later-arriving trains (trains T62, T64 in the example of FIGS. 8a through 8 c) need not slow appreciably in order to minimize the waittimes in the manner described above, those later-arriving trains canthen maintain full express service. However, in some cases, thearrangement of subway line SLINE will require full express trains toslow significantly in order to not be forced to wait for platform 50 toopen at the next express station. According to another embodiment of theinvention, as will now be described in connection with FIGS. 9 a through9 c, the available additional time can be used to further improveservice by including “semi-express” stations into the schedule.

FIG. 9 a illustrates an express interval along subway line SLINE betweenexpress stations E0 and E1. Local stations L1, L2, L3, L4 are locatedalong this interval. At the point in time illustrated in FIG. 9 a, trainT63 has arrived at express station E1, having provided local serviceover the interval between express stations E0 and E1. Train T65 is nextto arrive at express station E1, and has been providing express servicealong that same interval. According to the transformation embodiments ofthis invention, train T63 will provide express service over the intervalfollowing express terminal E1 (i.e., train T63 is an LE train), andtrain T65 will provide local service over that next interval (i.e.,train T65 is an EL train). Rather than unduly slow the travel velocityof train T65 to eliminate its wait time at express station E1, train T65makes one local stop along the interval between express stations E0 andE1, specifically at local station L3 in the example of FIG. 9 a. Bymaking this additional stop, the arrival time of train T65 can bemanaged so that it arrives at express station E1 “just in time”, astrain T63 pulls out of the station. In addition, local station L3receives the benefit of “semi-express” service, in that passengers mayboard and de-board train T65 at that station, and travel to expressstation E1 without making a stop at intervening local station L4.

FIG. 9 b illustrates a variation of this semi-express embodiment of theinvention, for the case of a three-train group of trains T66, T68, T70proceeding along the same interval. At the point in time shown in FIG. 9a, train T66 is stopped at express station E1, after having providedlocal service along the interval between express stations E0, E1 (andthus having stopped at each of local stations L1, L2, L3, L4). Train T66is an LE train, and such will provide express service along the intervalafter express station E1. Train T68 will be the next train to arrive atexpress station E1 after train T66 leaves; this train T68 has providedexpress service over the interval between express stations E0 and E1,and as such will be catching up to LE train T66 (optimally) as train T66leaves express station E1. As such, train T68 has made no stops alongthis interval since it left express station E0. In this example,however, third train T70 follows train T68, and is providing expressservice (and, indeed, will be an EL train at express station E1,beginning local service over the next interval). Because two trains T66,T68 are ahead of tail train T70 in this example, train T70 makes onelocal stop along the interval between express stations E0 and E1,specifically at local station L3 in this example. By making thisadditional stop, the arrival time of train T70 can be managed so that itarrives at express station E1 “just in time”, as train T68 pulls out ofthe station. In addition, local station L3 receives the benefit of“semi-express” service, in that passengers may board and de-board trainT70 at that station, and travel to express station E1 without making astop at local station L4. FIG. 9 b also illustrates an alternative forsecond train T68, in which it makes a semi-express stop at local stationL4 to eliminate its wait time at express station E1 (waiting for trainT66 to leave). Local station L4 in this case is also provided withsemi-express service, at little or no cost to the overall travel time oftrain T68 along subway line SLINE.

FIG. 9 c illustrates a similar example of semi-express operation, inconnection with a four-train group. In this example, train T72 is the LEtrain, and has arrived at express station E1 after having provided localservice along the interval. Train T74 is a train providing expressservice over the interval immediately following train T72, and willarrive at express station E1 just after train T72 has left. To moreefficiently manage the arrival of train T74 at express station E1, trainT74 has made one semi-express stop along the interval, at local stationL4 in this example. Train T76 will be the next to arrive at expressstation E1 after train T74 and, in this case, will make one semi-expressstop at station L3 (which is an earlier stop, west-to-east, along subwayline SLINE than is station L4 at which train T74 makes a semi-expressstop). Train T78 is the fourth train in this group, and will be the ELtrain at express station E1. Train T78 also makes a semi-express stop,at station L2 (which is earlier stop, west-to-east, than semi-expressstations L3 and L4). Optionally, train T78 can make another semi-expressstop along this interval, for example at local station L3, to furtherdelay its arrival at express station E1 until after train T76 has leftthe station. FIG. 9 c thus illustrates that no correlation necessarilyexists between the position of a train within a group and the number ofsemi-express stops made along an express interval. Rather, the number,timing, and locations of semi-express stations over an interval dependson the particular situation.

According to this embodiment of the invention, the addition ofsemi-express stops within an express interval provides additionalflexibility in the scheduling of the arrival of express service trainsat an express station. This additional flexibility enables productiveuse of any delay time involved in minimizing the wait time at an expressstation, by providing semi-express service at one or more stops alongthe express interval, thus providing both an additional train topassengers boarding at those stations, and in many cases providing afaster trip for those passengers to the next express station. It iscontemplated that system 20 can incorporate such semi-express stops intothe optimization that it carries out in connection with subway lineSLINE, incorporating such factors as passenger demand and the like. Inaddition, the particular arrangement of semi-express stops can bealtered from that shown in FIGS. 9 a through 9 c. These and otherconstraints and alternatives may be included in the schedule andmanagement optimization carried out by system 20.

Local to Express Train “Transformation” with “Passenger Relay”

In the embodiments of the invention described above, subway line SLINEand its express stations are operated in a first-in-first-out manner. Inthis approach, the first train of a group to arrive at an expressstation is the first to leave, making it impossible for a passenger totransfer from a later-arriving train in a group to an earlier-arrivingtrain in that group. While benefits of this invention are still attainedeven with that complication, subway line SLINE and its trains can beoperated in a manner that enables forward transfer of passengers in anefficient manner, according to other embodiments of this invention. As aresult, not only can passengers more efficiently travel from any localstation to any other local station, but as will become evident below,according to this embodiment of the invention, ambitious passengers areprovided with the ability to travel nearly their entire trip at thefaster express velocity, by making strategic forward-moving transfers atexpress stations.

According to these embodiments of the invention, the virtual passingprovided by local to express train transformation, as described above inconnection with FIGS. 6, 7 a through 7 c, 8 a through 8 c, and 9 athrough 9 c, enables passengers to forward transfer from train to trainat each express station. More specifically, these embodiments of theinvention enable passengers on an express train to transfer from an ELtrain (i.e., an express train that is transforming to a local train) toan LE train (i.e., a local train that is transforming to an expresstrain). In other words, passengers may remain on an express trainthroughout the duration of the trip, to the extent that the passenger istraveling the full length of intervals between express stations. As willbecome evident from this description of these embodiments of theinvention, according to this “passenger relay” approach, passengers areprovided with the option of actually traveling faster than the fastesttrain traveling along subway line SLINE. It is contemplated that thismode of travel will have most appeal to regular commuters who arefamiliar with the actions required on their part to make these forwardtransfers, and perhaps to younger commuters who are able to rapidlychange trains in a forward direction.

FIGS. 10 a through 10 d illustrate the operation of trains T80, T82 in atwo-train group, in making stops at platform 50 at express station E_(x)according to an embodiment of the invention in which passengers may makea forward train-to-train transfer. According to this embodiment of theinvention, platform 50 is made accessible to passengers in the rear-mosttrain of a group of trains before it is made accessible to thefront-most train in that group. At the point in time shown in FIG. 10 a,this forward transfer is facilitated by front-most train T80 (the LEtrain in this example) stopping with its rear portion at platform 50,and by rear-most train T82 (the EL train in this example) stopping withits front portion at platform 50. In this state, access from platform 50is provided to both of trains T80 and T82. More importantly, forpurposes of the passenger relay operation, platform 50 is made availableto some passengers in rear-most train T80.

For best efficiency, it is useful to control (or at least encourage)access to platform 50 during this initial stop so that only forwardtransfer passengers de-board rear-most train T82, and so that nopassengers board or de-board front-most train T80. FIG. 10 b shows thedesired relay passenger flow from the front half of train T82 toplatform 50, with those de-boarding passengers then moving toward thedowntrack side of platform 50. The doors to train T80 may remain closedduring this time, to prevent passenger ingress and egress. By limiting(or encouraging limited) passenger access to platform 50 with trainsT80, T82 sharing platform 50, the stop time required for this procedurecan be minimized.

Following the de-boarding by forward transfer passengers in FIG. 10 b,both trains T80, T82 close their doors, and then back up a portion oftheir lengths so that train T80 is then stopped along the length ofplatform 50. Passengers now board and de-board train T80 from and toplatform 50. In addition, those forward transfer passengers whode-boarded train T82 during the transfer stop of FIGS. 10 a and 10 b nowboard the front part of train T80, as shown in FIG. 10 c. In this way,those same passengers are in the correct position to de-board train T80to make a subsequent forward transfer to the next train ahead of trainT80, at the next express station E_(x+1), in the same manner as just nowaccomplished at express station E. Passengers in the front portion oftrain T80 can now de-board to platform 50 as desired. Upon completion ofthe boarding and de-boarding of train T80 in FIG. 10 c, train T80 thenleaves express station E_(x), providing express service (or semi-expressservice, if the approach described above relative to FIGS. 9 a through 9c is implemented) over the next express interval. Train T82 then pullsforward to platform 50 (FIG. 10 d), to allow its local passengers toboard and de-board in the conventional manner.

As shown in FIGS. 10 a through 10 d according to this embodiment of theinvention, passengers on an arriving express train that is about totransform into a local train (e.g., train T82) are permitted to transferto a train that is about to transform from local service to expressservice (e.g., train T80). These forward transferring passengers willthus arrive at their desired destination earlier than will train T82upon which they were riding. By continuing this forward transfer processat each express station, those passengers can ride along subway lineSLINE at express travel velocities over most if not all of the entirelength of their trip (short of any local interval necessary if the triporiginated or terminates at a local-only stations). Meanwhile, thosepassengers who do not wish to take advantage of the passenger relayoption still obtain the benefit of express service over a portion oftheir trip, namely over those intervals during which their train istraveling at express travel velocity. However, according to thisembodiment of the invention, the stop time at express station E_(x)could increase unless passenger access to platform 50 is controlled orencouraged to take place in the manner described above.

FIGS. 10 e through 10 g illustrate another implementation of thisembodiment of the invention, in which the passenger relay is limited toa few forward cars of the arriving EL train, but in which passengermovement among the cars of a given train is permitted (and is physicallypossible, within the constraints of passenger loading within eachtrain). With the constraint of intra-train passenger movement relaxed,the time required for passenger transfer and loading/unloading atexpress stations can be reduced. FIG. 10 e illustrates a first stage ofthe process, in which LE train T80 and EL train T82 are first stopped atplatform 50 of express station E. In this implementation, each of trainsT80, T82 have ten cars, and the initial stop of LE train T80 at platform50 places only a selected number of the rear-most cars (e.g., eightcars) at platform 50; the remaining forward-most cars (e.g., two cars)are past platform 50 in this initial stop. Later-arriving EL train T82stops at platform 50 behind train T80, and its forward-most cars (e.g.,two cars) are aligned at platform 50. This initial stop allowspassengers to begin making the relay between EL train T82 and LE trainT80, but only from these forward-most cars. These passengers de-board ELtrain T82, and walk the length of platform 50 to an area correspondingto the forward-most cars of LE train T80, but they do not board trainT80 at this time.

Trains T80, T82 both back up after the operation of FIG. 10 e, to theposition shown in FIG. 10 f in which all cars of LE train T80, includingthe forward-most cars, are aligned with platform 50. Boarding andde-boarding of train T80 is now permitted, relative to all cars. Duringthis portion of the stop, the relay passengers who de-boarded EL trainT82 (FIG. 10 e) can now board the forward-most cars of LE train T80,along with the other boarding and de-boarding passengers. LE train T80can then leave station E_(x) upon completion of this process, and beginexpress service over the next express interval; after train T80 leaves,EL train T82 pulls forward to platform 50 for its boarding andde-boarding operations (including the boarding of LEL transferringpassengers from train T80), as shown in FIG. 10 f. To assist in theflexibility of this passenger relay operation, passengers on train T80can now move from car-to-car, as suggested by the arrow in FIG. 10 g. Inthis way, LEE and LEL passengers who boarded train T80 during theprevious express interval can move into the forward-most cars and begintheir passenger relay journey; meanwhile, those passengers who will betransferring to local service at the next express station can move intothe rear-most cars to reduce overcrowding. It is contemplated thaton-train displays, or perhaps also the ticketing (e.g., e-ticketing)process can instruct individual passengers regarding their optimalmovement from car-to-car within a train, as well as from train-to-trainas discussed above.

Substantial time can be saved in the stops at express stations accordingto this implementation of FIGS. 10 e through 10 g. The time savingsstems primarily from the reduced length over which the trains must backup to complete the transfer. And, as discussed in this specification,because express station stop times are repeated multiple times over thelength of subway line SLINE, and are directly included as an adder toeach passenger's travel time, reduction in the express station stop timeis of particular importance in improving passenger and train travel timealong subway line SLINE, and thus passenger throughput.

It is of course contemplated that variations on the manner in which thepassenger relay process is enabled at each express station, includingthe number of rear-most cars to be aligned at each express stationplatform for a given passenger demand and train density, can vary fromtime-to-time during the day. Indeed, it is contemplated that thealignment of trains at express station platforms to permit passengerrelay operations can be optimized by system 20 in its generation of theschedule and operational parameters within the overall process of FIG. 3b.

The passenger relay concept can be extended to train groups of more thantwo trains. FIGS. 11 a through 11 c illustrate the stop operation atexpress station E_(x) for the example of a three-train group of trainsT84, T86, T88. Front-most train T84 is the LE train in this group, andrear-most train T88 is the EL train in this group; middle train T86provides express service over both intervals, before and after expressstation E. The first stage of the stop at express station E_(x) isillustrated in FIG. 11 a, in which train T84 pulls past platform 50, andtrains T86, T88 both align at platform 50 so that access is provided toportions of both trains simultaneously. This stop position in FIG. 11 aallows forward transfer passengers to de-board EL train T88, and enablespassengers to both board and de-board train T86 from platform 50. InFIG. 11 b, a next stage in this stop has trains T84, T86 both alignedwith platform 50. This allows passengers to board and de-board therear-most portion of train T84. In addition, during this time, theforward transfer passengers from EL train T88 are now able to boardeither the rear-most portion of train T84 or the front-most portion oftrain T86. Those forward transfer passengers who will be making anotherforward transfer at the next stop will wish to board the front-mostportion of train T86, as this train will be an EL train at the nextexpress station E_(x+1) and thus these passengers will wish to de-boardtrain T86 at the first stage at that station (as shown in FIG. 11 a).The stop at express station E_(x) for this three-train group is shown inFIG. 11 c, in which EL train T88 stops along the length of platform 50after trains T84, T86 have left the station; local passengers can thenboard and de-board train T88.

The operation of a stop at express station E_(x) for a two-train groupof trains T90, T92 is illustrated in FIGS. 12 a through 12 c, for oneexample of this embodiment of the invention. In this example, each oftrains T90, T92 has a length that is about one-half the length ofplatform 50, and in this case each train consists of four train cars. Inthe first stage of this stop shown in FIG. 12 a, front-most train T90(the LE train) occupies the front half of platform 50, and rear-mosttrain T92 (the EL train) occupies the rear half of platform 50. In thisfirst stage, passengers terminating their trip at express station E_(x)can de-board train T90; express passengers (EEE passengers) who wish toboard an express train at station E_(x) can board train T90 at thistime, as shown in FIG. 12 a. Those passengers wishing to transfer fromexpress service (train T90) to local service over the next interval (ontrain T92) also deboard train T90 during this first stage of the stop.Also at this point in time, those passengers wishing to make the relayfrom EL train T92 to LE train T90 (i.e., who wish to continue from oneexpress train to the next) de-board train T92 to platform 50, but remainat the rear portion of platform 50. In a next stage of the process,shown in FIG. 12 b, trains T90 and T92 move backward, aligning train T90with the rear portion of platform 50. The forward transfer passengersfrom EL train T92 can now board train T90. The final stage of this stopis shown in FIG. 12 c, with EL train T92 stopped along the front portionof platform 50 to receive local passengers; by this time, train T90 hasalready left express station E.

In this approach illustrated in FIGS. 12 a through 12 c, passenger relayis accomplished in a manner that minimizes the necessary movement of therelaying passengers, at a cost of requiring the trains to move back andforth along the station platform. According to another approach, as willnow be described in connection with FIGS. 12 d and 12 e, the stop timeof the trains at the express stations is minimized, at a cost ofrequiring the relaying passengers to move along the station platform.

FIG. 12 d shows express station E_(x) at a first stage of the stop of LEtrain T90 and EL train T92, both of which have a length approximately ofone-half the length of platform 50. In this first stage, train T90occupies the front half of platform 50 and train T92 occupies the rearhalf of platform 50. At this time, as shown in FIG. 12 d, passengersterminating their trip at express station E_(x) can de-board train T90,and EEE passengers can board train T90. Also at this point in time,those passengers making the relay from EL train T92 to LE train T90(i.e., who wish to continue from one express train to the next) de-boardtrain T92 to platform 50 and move along platform 50 directly over totrain T90, which they board. In the second stage of the stop, as shownin FIG. 12 e, train T92 stops at the front portion of platform 50 aftertrain T92 has left express station E_(x), to receive local passengers,including those who de-boarded train T90 during the first stage of thestop. As a result of this approach, LE train T90 only has to make asingle stop along platform 50, because the relay passengers move fromtrain T92 to train T90, rather than train T90 moving to the relaypassengers as in the case of FIGS. 12 a through 12 c.

FIG. 12 f illustrates another alternative to these two approaches, inwhich both transferring and relaying passengers move from train totrain, allowing both the LE train and the EL train to make a single stopat express station E. FIG. 12 f illustrates the passenger movementbetween LE train T90 and EL train T92; the movements of passengersboarding and de-boarding either train from or to express station E_(x)are shown by horizontal arrows in FIG. 12 f. In this example, relaypassengers exit EL train T92, walk along platform 50, and board LE trainT90; conversely, express-to-local transferring passengers exit LE trainT90, walk along platform 50 in the opposite direction, and board ELtrain T92. It is contemplated that markings or temporary barriers orsome other physical assistance to the relay and transfer passengers atplatform 50 can facilitate the passenger movements involved. Followingthe passenger movement in this single stop at platform 50, both trainsT90, T92 can depart express station E. In this regard, it may be usefulfor closed-circuit television or some other real-time monitoring ofexpress station E_(x) can be used to allow sufficient time for allmovement between trains and other boarding activity, such that thedeparture of trains T90, T92 can be done as soon as possible whileallowing passengers to complete their transfers.

As discussed above, the number of trains per group can be increasedduring peak times, in order to improve passenger throughput andpassenger travel times, without necessarily changing the schedule oflocal service, considering that local trains are the pacemakers alongsubway line SLINE. It is further contemplated that express service canbe provided along subway line SLINE even if demand in off-peak times isvery low, and it is further provided that transfers and passenger relayoperation can be enabled even with that low passenger demand, as willnow be described in connection with FIGS. 12 g and 12 h.

In the alternative shown in FIG. 12 g, each of LE train T94 and EL trainT96 at express station E_(x) is a half-length train, relative to thelengths shown in FIGS. 12 a through 12 f. Similarly as in the case ofFIG. 12 f, FIG. 12 g illustrates the passenger movement between trainT94 and T96 in both directions. As such, relay passengers exit EL trainT96, walk along platform 50, and board LE train T94 simultaneously withexpress-to-local transferring passengers exiting LE train T94, walkingalong platform 50 in the opposite direction, and boarding EL train T96.Following the passenger movement in this single stop at platform 50 (andany boarding and de-boarding of originating or terminating passengers atexpress station E_(x), not shown in FIG. 12 g), both trains T94, T96depart express station E_(x) in succession. Similarly, FIG. 12 hillustrates the same operation in connection with LE train T98 and ELtrain T99, each of which are minimum-length trains constituting a singlecar in each. Also in this example, each of trains T98, T99 make a singlestop, and all relay and express-to-local transfers are made during thatstop, along with boarding and de-boarding from and to express station E.These shorter-length trains as shown in FIGS. 12 g and 12 h enable thesubway operator to continue to provide express service withoutdisrupting the local train schedule, even at off-peak times in whichridership is otherwise very low.

In each of these examples shown in FIGS. 12 a through 12 h, passengersfrom the rear-most train of a group, that rear-most train transformingfrom express to local service at the express station, can transferforward to a train that will be providing express service over the nextinterval. This passenger option allows these relay passengers to travelfaster than any given train along subway line SLINE, while also allowingpassengers not wishing to make the forward transfer with shorter traveltimes as well.

It is contemplated that system 20 will be able to comprehend the forwardtransfer option and processes, and to notify passengers of the optionand the boarding (i.e., car assignment) and transfer proceduresnecessary to optimally use passenger relay for each passenger's specificjourney. Graphics or video displays on the trains or at the stations canbe driven by system 20 to advise passengers of these options andprocedures, or system 20 can advise the passengers via the ticketingprocess (especially if point-to-point ticketing is used).

FIGS. 13 a through 13 d show one example of the manner in which system20 can communicate boarding and transfer instructions to passengers at astation of origin, and perhaps also at an express station at which arelay or express-to-local transfer is permitted. As shown in the planview of FIG. 13 a, platform 50 is conceptually divided into two equallength platform portions 50 b, 50 p, each color-coded blue and pink,respectively, with blue platform portion 50 b downtrack from pinkplatform portion 50 p. At the point in time shown in FIG. 13 a, twotrains T102, T104 are stopped at platform 50, with train T102 alignedwith blue platform portion 50 b and train T104 aligned with pinkplatform portion 50 p. FIG. 13 b is an elevation view of the middleportion of platform 50 at which trains T102 and T104 abut one another atthis stop; as shown in FIG. 13 b, car C102 e is the last car of trainT102 and car C104 a is the first car of train T104. Graphics displays106 b, 106 p are mounted above platform 50, overhanging blue and pinkplatform portions 50 b, 50 p respectively, to provide well-visibleinstructions to passengers boarding cars C102 e, C104 a. FIGS. 13 c and13 d illustrate an example of the information displayed on graphicsdisplays 106 b, 106 p, respectively, at the time that trains T102, T104are stopped at this station. Each of graphics displays 106 b, 106 pdisplay the platform portion color (e.g., blue and pink), the trainnumber of the trains current stopped at those platform portions 50 b, 50p (or approaching the station, if not yet arrived), and a list of thosestations at which a passenger boarding a train stopped or soon to stopat platform portions 50 b, 50 p will be able to stop without a transfer.In embodiments of this invention, system 20 will drive graphics displays106 b, 106 p with the appropriate information for the current orupcoming stop at that particular station, to assist passengers inboarding the optimum train car or transferring between trains toaccomplish their trip in the most efficient manner.

In addition, system 20 may alter the particular processes and stagesimplemented at the express stations from those described above inconnection with FIGS. 10 a through 10 d, 11 a through 11 c, and 12 athrough 12 c, as appropriate to further optimize the operation of thesubway system for passenger travel time, passenger throughput,infrastructure and rolling stock optimization, and the like. Thoseupdates can, of course, also be communicated to passengers by way ofat-station graphics displays 106 b, 106 p (FIGS. 13 a through 13 d), byway of on-train graphics displays, or in the ticketing process asdescribed above.

Regardless of whether the passengers make the forward transfers, becauseof the ability to travel at least part of the trip on subway line SLINEat express velocity V_(exp), it is contemplated that the passengertravel time on subway line SLINE will be reduced for many, if not all,passengers according to this embodiment of the invention. It is alsocontemplated that the ability of system 20 according to this embodimentof the invention, in displaying schedules and train assignments, andperhaps individual tickets for specific station-to-station trips, canreduce confusion on the part of the subway passengers in navigatingsubway line SLINE, especially for commuting trips in which thepassengers can become used to the best way to make their desired trips.Overall efficiency in the travel of many passengers, and in theutilization of the subway system including reduction in overcrowding byimproving the passenger throughput, is therefore expected to be readilyattained through use of this embodiment of the invention.

Schedule and Operational Optimization

General Methodology

As described above relative to FIGS. 3 a and 3 b, process 38 is executedby system 20 to derive a schedule for the trains along subway line SLINEso that express and local trains traveling in the same direction meetonly at express stations. It is contemplated, according to thisinvention, that process 38 will be carried out by system 20 according toan optimization algorithm, in which a cost function is established andminimized by iteratively changing parameters that define the schedulebeing derived. The particular cost function being minimized in derivingthe schedule may seek to optimize any one or more of a number ofparameters, such as passenger throughput, passenger travel times over apopulation of passengers, infrastructure demands, and the like. Scheduleparameters that may be changed in each iteration include such factors astrain departure times, train interval velocities, number of trains in agroup, boarding and de-boarding times and sequences at express and localstops, and the like.

A close relationship exists between a subway line system and thepassenger volume on a given subway line, in that each depends on theother. The definition of a schedule for the subway line system, andparticularly the optimization of that schedule, requires interacting thesubway line system itself with the passenger volume on that line.Efficiency of the system in light of passenger demand is best served bydefining applicable system parameters, and the characteristics of thepassenger volume. According to embodiments of this invention, theseparameters and characteristics can be analyzed in a manner correspondingto the following Table 2:

TABLE 2 Train density Theor. Express Train (per pass. Pass. Train Trainstrains length express Local Pass. travel travel group Passing per per(wrt station train thruput time time pass. Technique Manner FIGS. groupgroup platform) interval) equiv. per train saving saving thruputPhysical Side-  1b-1d; 2 1 1 3 4 1.3 50% ~45% 2.66 passing track 7e-7g 32 1 4 6 1.5 50% ~43% 4.5 4 3 1 5 8 1.6 50% ~40% 6.4 Side- 4a-5o 2 1 1 34 1.3 50% ~45% 2.66 by-side 3 2 1 4 6 1.5 50% ~43% 4.5 station 4 3 1 5 81.6 50% ~40% 6.4 Local trains only 7d 1 0 1 2 2 1  0%    0% N/A VirtualLocal to 7a & 7e 2 1 1 3 4 1.3 25% ~20% 2.66 passing express 7b & 7f 3 21 4 6 1.5 33% ~30% 4.5 xform 7c & 7g 4 3 1 5 8 1.6 41% ~35% 6.4 Local to10a-10g 2 1 1 3 4 1.3 50% ~45% 2.6 express 11a-11c 3 2 1 4 6 1.5 50%~45% 4.5 xform 12g-12h 2 1 0.5 3 4 0.66 50% ~45% 1.33 with pass. 2 1 0.23 4 0.26 50% ~46% 0.53 relay 2 1 0.1 3 4 0.13 50% ~47% 0.26Table 2 summarizes performance characteristics for examples ofembodiments of the invention described above. More specifically, the“Passing Technique” column groups the approaches of those methods intothose in which express trains physically pass local trains at an expressstation, and those in which the passing is “virtual” in the sense thatspecific physical trains transform their service from local-to-express,and express-to-local, at express stations. The detailed descriptioncorresponding to each implementation is indicated by way of reference toits corresponding Figure or Figures. Various performance parameters foreach individual implementation are shown in a normalized form, relativeto conventional “local-only” service in which all trains on the subwayline provide local service. In Table 2, the column “Trains per group”designates the number of trains in each group that meet at an expressstation; the column “Express trains per group” indicates the number oftrains providing express service in each group, and each of theseimplementations assume a single local train in each group. The “Trainlength” column indicates the length of each train relative to a standardplatform length. Based on those assumptions, the “train density” isindicated in the next column, referring to the total number of local andexpress trains physically present over each express interval.

Based on those assumptions, the remaining columns beginning with “Localtrain equivalent” are essentially calculated values. The column “Localtrain equivalent” is derived by considering the number of trains withinan express interval are express trains (assumed to be traveling at twicethe average travel velocity of a local train), in combination with thetrain density over an interval. In short, “Local train equivalent” iscalculated as:

(Local train equivalent)=2+2*(Express trains per group)

This is because two local trains are present within each expressinterval at any given time. For example, a two-train group results intwo local trains and one express train within an express interval at anygiven time; because the express train is traveling at twice the travelvelocity as the local trains, an express train can transport twice asmany passengers than can a local train over a given time duration.Therefore, the equivalent passenger capacity in terms of local-onlytrains is four. The column “Passenger throughput per train” reflectsthis same parameter in terms of the Local train equivalent divided bythe Train density within the express interval.

The “Theoretical passenger travel time savings” column refers to thetime that a passenger would save by virtue of the ability to travel atexpress travel velocities, relative to traveling via local-only service,and assuming no additional time required for physical or virtual passingat the express stations. For example, in two-train groups operatedaccording to the physical passing technique, a passenger would betraveling at express travel velocity for the duration of his or herjourney, in which case the travel time savings would be 50% (expresstravel velocity being twice local travel velocity). For two-train groupsinvolving virtual passing (and no passenger relay), a passenger would betraveling at express travel velocity over alternating express intervals(i.e., about half the time), during which time his or her travelvelocity would be twice that of the local travel velocity over the otherintervals; this amounts to a 25% theoretical passenger travel timesaving. And for two-train groups involving virtual passing withpassenger relay, a passenger becomes able to travel at expressvelocities over the full duration of the journey, thus achieving thetheoretical travel time saving of 50%.

It is contemplated that those skilled in the art can readily comprehendthese performance criteria as summarized, by way of example, in Table 2.Among other conclusions, it can be seen from Table 2 that the physicalpassing techniques can theoretically attain a passenger travel timesaving of 50%, as all express trains continue to provide expressservice, at express travel velocity, over the entire length of thejourney. In addition, Table 2 summarizes that the passenger relay methodapplied to the virtual passing techniques can also attain this 50%theoretical passenger travel time saving. According to Table 1, becauseof the ratio of express and local train operation intervals, thetheoretical passenger travel time saving for the two, three, and fourtrain group virtual passing (without passenger relay) case are 25%[(3/6)*0.5*100], 33% [(4/6)*0.5*100], and 41% [(5/6)*0.5*100],respectively. And as described above, the virtual passing techniques canbe applied to existing subway lines, without requiring construction orexcavation or other changes to infrastructure as necessary in thephysical passing context.

Extra-Train Delay Time

As mentioned above, however, the theoretical passenger travel timesaving assumes no time is involved in the passing operations at expressstations. This is, of course, unrealistic for both the physical andvirtual techniques, considering that time must be allotted for passengertransfer (local-to-express, and express-to-local). Table 2 includes thecolumn “Passenger travel time saving”, which includes the effect of thedelay time for passenger transfer at express stations, as will now bedescribed.

As a concept, an understanding of the delay time required for passengertransfer is simple. However, it has been observed, in connection withthis invention, that it is cumbersome to actually estimate thisextra-train delay time (EDT) to any precision, because EDT depends onthe passing method, on the number of trains in a group, and on otherfactors including train length relative to the platform length. Morespecifically, one must estimate the stop time for a local train at alocal station (LLST), and the stop time for a local train at an expressstation (LEST); the difference between the local-train express-stationstop time (LEST) and the average local train stop time (ALST) determinedas the average local-train local-station stop time (LLST) over all ofthe local stations of subway line SLINE, which tends to be a stablequantity. The calculation of EDT differs between the physical passingand virtual passing methods. Under the physical passing case, in whichlocal trains remain local and express trains remain express, thequantity LEST can be defined as the time elapsed between the arrival ofthe local train at the express station, and the departure time of thatlocal train from the express station, assuming the number of trains pergroup exceeds one (i.e., at least one express train passes the localtrain at the express station). Under the virtual passing case, thequantity LEST is defined as the time elapsed from the LE train (i.e.,the first train in the group) arriving at the express station and thedeparture of the EL train (i.e., the last train in the group). Thequantity EDT for both cases is then defined as EDT=LEST−ALST.

Consistent with these definitions and based on the description of thesepassing methods in this specification, one can deduce that the quantityEDT will vary from one passing method to another, and also will varywith the length of the trains involved. Those variations in EDT will bereflected in the proximity of the “Passenger travel time saving” valueto the “Theoretical passenger travel time saving” shown in Table 2 forthe various operational methods. That proximity will result from thecalculations of total passenger travel time over subway line SLINE,based on the schedules derived by system 20 in connection withscheduling process 38, as will now be described.

As described above, scheduling process 38 is executed by system 20 toderive and, if desired, modify the scheduling of trains along subwayline SLINE in response to passenger data 33, train data 35, and stationdata 37, and according to the definition of certain stations and trainsas express and local stations and trains, respectively. It iscontemplated that scheduling process 38 will serve to optimize thederived and modified schedule according to a criteria selected by thesubway system operator. It is further contemplated, according to thisinvention, that a particularly beneficial approach to scheduling process38 is to optimize the schedule in order to minimize total passengertravel time over subway line SLINE. The passenger travel time beingminimized may be that for a trip over the entire length of subway lineSLINE, or alternatively may be a cumulative or average passenger traveltime value taken over a typical population of passengers, or some otherpopulation. Fundamentally, this optimization of passenger travel timedepends on a wide range of factors, including the particular passingmethod used (i.e., physical or virtual passing); the lengths of trainsand platforms; the time of day; the type of day such as workday,weekend, or holiday; passenger demand by station; and the like. Theseadditional factors are, in general, dependent on the characteristics ofthe subway system and the city being served, and as such can beconsidered as installation-dependent. For purposes of this description,however, it is believed useful to describe some of the factors involvedin the optimization of the schedule from the standpoint of minimizingpassenger travel time, as it is contemplated that this optimization willbe an important goal of implementations of embodiments of this inventionin practice.

For purposes of simplicity and clarity of this description, the abovediscussion summarized in the column “Theoretical passenger travel timesavings” of Table 2 has been based on two assumptions: first, that thelength of each train and the length of the platform at each station areeach zero; and second, that all trains of a group arrive at and departfrom each express station at the exact same time. In effect, theextra-train delay time (EDT) was assumed to be zero. Of course, inpractice, those two assumptions do not hold.

In order for scheduling process 38 to actually minimize passenger traveltime, according to embodiments of this invention, additional parametersare considered. For reference purposes, it is useful to consider thebaseline operational times of a local-only train in traveling an expressinterval, including the time involved in making a stop at an expressstation. This local-only travel time (LETT) of the i^(th) expressstation can be more accurately described as the difference between thetime at which the local-only train arrives at express station E_(i)(e.g., the time at which the head car of this arriving eastbound trainreaches the easternmost endpoint of platform 50 e of FIG. 4 a), time atwhich that train departed the previous express station E_(i−1) (e.g.,the time at which the head car of this departing eastbound train leavesthe easternmost endpoint of platform 50 e). Also under consideration forthat interval is the time required for the local-only train to make itsstop at express station E_(c). For purposes of this description, one canuse the average local train express station interval stop time (ALST),which tends to be a stable quantity. The local-only trainexpress-station-interval operation time (LEOT) can then be defined asthe sum:

LEOT₁=LETT₁+ALST

This baseline local-only train operation time of the i^(th) expressstation interval LEOT_(i) is also a factor in the operation of a grouptrain according to embodiments of this invention described above, exceptthat the group train express-station-interval operation time (GEOT_(i))also requires consideration of the extra-train delay time (EDT)amounting to the additional delay time of a group train at an expressstation:

GEOT_(i)=LEOT_(i)+EDT

As mentioned above, EDT varies according to the passing method used, andalso varies with the number of express trains within the group, suchthat EDT=EDT(m, j), where m refers to the passing method and j indicatesthe number of trains within a group. In any case, extra-train delay timeEDT depends on such factors as the not-insignificant time required forthe head of the train to move the length of the platform (theinstantaneous velocity of the train being relatively slow, for safetyreasons) and also the time required for the tail of a preceding train toclear the length of the platform as that train departs (theinstantaneous velocity of that train also being relatively slow).

As discussed above, in the general sense, the local-only train operationtime LEOT will spatially vary, being different for different expressintervals:

LEOT₁≠LEOT₂≠LEOT₃≠ . . .

An example of the spatial variation of train operational time forlocal-only trains, over six express intervals, is illustrated in FIGS.14 a and 14 b, in which the horizontal axis is elapsed time (rather thandistance or location). Similarly, an example of the spatial variation oftrain operational time for group trains over these intervals isillustrated in FIGS. 14 c and 14 d. FIGS. 14 a through 14 d use theaverage local station stop time ALST for each interval, such an averagevalue being constant over the intervals by definition; FIGS. 14 c and 14d use a constant extra-train delay time value EDT for each expressstation, for simplicity of this description.

As evident from a comparison of FIGS. 14 c and 14 d with FIGS. 14 a and14 b, GEOT_(i)>LEOT_(i) for each interval, reflecting that a non-zeroextra-train delay time value EDT at each express station E0 through E6.In other words, if one looks to train travel time alone, it appears fromthese FIGS. 14 a through 14 d that the total local train group traveltime (TGOT) according to embodiments of this invention is larger (i.e.,slower) than the total local train travel time (TLOT) under local-onlyservice. This means that the total passenger travel time of “LLL”passengers defined above, who travel exclusively on local service trainsfor the duration of their journey of at least one full express interval,will necessarily be slower on subway lines that implement embodiments ofthis invention. On the other hand, according to embodiments of thisinvention, the passenger travel time of those passengers (EEE, EEL, LEE,LEL) who travel at least one express interval using express service willbe less than (i.e., faster than) that of the LLL passengers. Thisdifference between train travel time and passenger travel time isimportant in the implementation of scheduling process 38, to ensure thatthe desired optimization parameter (e.g., passenger travel time ratherthan train travel time) is selected for minimization.

The above discussion uses average local station stop time ALST, which isconstant over each express interval. However, in practice, it iscontemplated that the local-only train stop time at each express stationi (i.e., time LLST_(i)) will vary from express station to expressstation, because the time that a given train is stopped at a station inmodern subway systems varies with the number of passengers boarding andde-boarding the train at that station. In short, the local-only trainstop time LLST_(i) at express station E, will vary with the time of day:longer during rush hours, and shorter during non-rush hours. Fieldobservations from conventional subway lines indicate that the stop timeof a local-only train at a station during rush hour can be several timeslonger than the stop time of the same train during non-rush hour. Assuch, proper determination of the average local station stop time ALSTconsiders these spatial and temporal variations:

${{ALST}(\tau)} = {\frac{1}{N_{s}}{\sum\limits_{i = 1}^{N_{s}}{{LLST}_{i}(\tau)}}}$

where τ is a variable corresponding to the time of day, and N_(s) is thetotal number of local stations along subway line SLINE. In addition, itis also contemplated that the local-only travel time LETT may also varywith the time of day, as some extra-train delay time may occur at somelocal stations. The variation of these parameters with time of day τ andamong express intervals i is illustrated in FIGS. 15 a through 15 d.

This variation of operational times with the time of day can beapproached in various ways within scheduling process 38. For example, ifthe schedule is to be derived using operational times that are fixed(for scheduling purposes) over the day, then scheduling process 38 canbe optimized by minimizing error FSOE(τ) defined by:

$\begin{matrix}{{{FSOE}(\tau)} = {{\sum\limits_{k = 1}^{K_{s}}\overset{\_}{{GEOT}_{k}(\tau)}} - {\sum\limits_{k = 1}^{K_{s}}{GEOT}_{k}}}} \\{= {\overset{\_}{{TGOT}(\tau)} - {TGOT}}}\end{matrix}$

where K_(s) is the number of express stations, where the valuesGEOT_(k)(τ) and TGOT(τ) are the actual operation times observed inpractice, as varying with time over the time of day, and where thevalues GEOT_(k) and TGOT are those defined by the fixed schedule.Another approach available within scheduling process 38 is to vary theoperational schedule dynamically over the time of day, in that thevariations with the time of day are incorporated into the determining ofthe schedule in the first place. According to that approach, schedulingprocess 38 can be optimized by minimizing error DSOE(τ) defined by:

$\begin{matrix}{{{DSOE}(\tau)} = {{\sum\limits_{k = 1}^{K_{s}}\overset{\_}{{GEOT}_{k}(\tau)}} - {\sum\limits_{k = 1}^{K_{s}}{{GEOT}_{k}(\tau)}}}} \\{= {\overset{\_}{{TGOT}(\tau)} - {{TGOT}(\tau)}}}\end{matrix}$

where the scheduled values GEOT_(k)(τ) and TGOT(τ) as scheduledthemselves vary with the time of day.

For example, if an average local-only stop time ALST(τ) is defined asthat stop time at τ=8:00 am, then the error value FSOE(τ) evaluated atτ=8:00 am will be close to zero, but the error value FSOE(τ) evaluatedat τ=11:00 am will be substantial. Conversely, if dynamic scheduling isused in scheduling process 38 to define the schedule at τ=8:00 am usingthe average local-only stop time ALST(τ=8:00 am), and to define theschedule at τ=11:00 am using the average local-only stop timeALST(τ=11:00 am), then the error DSOE(τ) will be much lower.

Scheduling process 38 can be further refined by applying a seconddimension of temporal variation, considering the difference in passengerload from day-to-day. In other words, differences between normalworkdays, weekends, and holidays, may be included within theoptimization process, by considering parameter such as averagelocal-only stop time ALST(τ,κ) to be defined not only with respect totime of day τ, but also with respect to day of the week (or month, oryear, or both) κ. FIGS. 16 a through 16 d illustrate the travel timelines of FIGS. 14 a through 14 d and 15 a through 15 d in which thevarious illustrated parameters vary spatially (i.e., with expressinterval i) and also temporally with respect to time of day τ andcalendar day κ.

Observations

The relative efficiencies of various approaches to the synchronizedexpress and local trains, according to these embodiments of theinvention, can thus be readily compared by system 20. For example, thephysical passing embodiments of this invention utilizing side-tracks areexpected to have a substantially different passenger transfer time thanthat of the virtual passing embodiments of this invention in whichtrains transform between providing express and local service. Of course,in those embodiments of the invention involving the transformation oftrains between local and express service, the passenger travel time willbe affected by the numbers of intervals that the passenger will betraveling at local travel velocities versus express travel velocities,the particular velocities of those intervals (see FIG. 3 d), and whetherthe passenger relay (or forward transfer) option is available andutilized by the passenger. In any event, it is believed, in connectionwith this invention, that the minimization of passenger travel time willbe best accomplished by the minimization of passenger transfer times atexpress stations, given that the travel velocities will tend to beconstrained. Certain general concepts have been identified by analysisof these factors, in connection with the minimization of passengertravel time in such train systems, as will now be summarized for thebenefit of the reader.

In a general sense, based on qualitative analysis, it is contemplatedthat physical passing techniques will result in shorter passenger traveltimes than achievable by virtual passing techniques, for longerpassenger journeys (in terms of the number of express intervals).Conversely, for shorter journeys, virtual passing techniques provideshorter passenger travel times. Of course, as mentioned above, theinfrastructure cost of virtual passing techniques is much lower thanthat involved in enabling physical passing at express stations; inaddition, greater flexibility is provided by the virtual passingtechniques.

In this regard, analysis has shown, according to this invention, thatfor the embodiments of the invention in which a side track enablesphysical passing of local trains by express trains, as described aboverelative to FIGS. 1 b through 1 d, 3 a through 3 k, 4 a through 4 e, and5 a through 5 k, one can minimize the extra-train delay time EDT atexpress stations by selecting those stations at which the fewest numberof passengers board and de-board express trains from outside of subwayline SLINE. In other words, if the stop time at an express station isdevoted primarily to the transfer of passengers between express andlocal trains, with little time required for the boarding of newpassengers and the de-boarding of departing passengers, the expressstation passenger transfer time ESPT can be minimized. Because the samelocal-to-express (and vice versa) transfers will be occurring at thatexpress station regardless of the passenger demand of that station, theoverall passenger travel time for most passengers will be reduced if thenew and departing passengers from the express station are minimized.

In connection with the embodiments of this invention utilizing virtualpassing at express stations, by way of transforming trains fromproviding local service to providing express service, and vice versa,analysis has shown that the express station passenger transfer time ESPTcan be minimized, and thus the overall passenger travel time minimized,also by selecting those stations at which the fewest number ofpassengers board and de-board express trains from outside of subway lineSLINE as the express stations. In other words, use of the mostlightly-used stations as express stations will optimize passenger traveltimes, for similar reasons as described above.

Also in connection with the embodiments of the invention in whichvirtual passing by transforming trains from local to express, and viceversa, overall passenger travel time can be minimized by maximizing theuse of the express mode by as many passengers as possible, over as muchof their respective trips as possible. One way in which this can beaccomplished is the use of semi-express stations, such as describedabove relative to FIGS. 9 a through 9 c, because passengers boarding ata semi-express station immediately board an express train inmid-interval. However, the passenger boarding and de-boarding time at asemi-express station does not significantly impact the overall passengertravel time for any passenger; those passengers boarding and de-boardingat the semi-express station obtain the benefit of longer express traveldistances (at necessarily higher travel velocity) than they wouldexperience on a local train, and the stop time at the semi-expressstation does not impact the express station passenger transfer time ESPTat the full express stations. Indeed, the reason for including asemi-express station in the first place is to avoid excessive train waittimes at the next express station. Accordingly, analysis has shown thatit is optimal to select those local stations with the highest passengertraffic (i.e., the highest number of passengers boarding andde-boarding) as the semi-express stations. The time required for thislarge number of passengers to board and de-board does not adverselyaffect the overall passenger travel time along subway line SLINEgenerally.

Also in connection with the embodiments of the invention in whichvirtual passing by transforming trains from local to express, and viceversa, analysis has shown that maximization of the passenger expressmode is improved by increasing the number of trains in a group, but at acost of increased express station passenger transfer time ESPT. Atradeoff therefore exists between the benefit of adding another train tothe number of trains in a group, and this cost of increased extra-traindelay time EDT. It has been found, through this analysis that, in manyreal-world cases, the use of three-train groups (two express trains forevery local train) will be optimal, as it permits the greatest number ofexpress passengers on the average without unduly lengthening the expressstation passenger transfer time ESPT and thus the overall passengertravel time.

Other optimization techniques and concepts will become apparent to thoseskilled in the art having reference to this specification, upon applyingembodiments of this invention to specific subway lines and systems,under real-world conditions.

Comparison of the various methods summarized in Table 2 above, andparticularly the proximity with which the value in the column “Passengertravel time saving” approaches the value in the column “Theoreticalpassenger travel time saving”, can thus be made to determine the gainsin efficiency obtained by the various methods and approaches. Ofparticular interest are the results of the shorter trains in thebottom-most rows of Table 2, corresponding to the virtual passingimplementations described above in connection with FIGS. 12 a through 12h. As the trains become shorter and shorter in length, relative to thelength of the platform, the actual “Passenger travel time saving” valuesapproach the “Theoretical passenger travel time saving” values. It iscontemplated that these highly efficient methods can be used duringoff-peak times of the day, and during off-peak days in theweek/month/year, such that subway line SLINE can be operated in a highlyefficient manner, with excellent passenger travel times, and with areduction in the operating cost because of the reduced length of trainsinvolved (and thus corresponding reductions in fuel consumption, laborcosts, and the like).

Also as evident in Table 2, the column labeled “Train group passengerthroughput” contains values that vary among the various implementations.This value is defined, for purposes of Table 2, as the product of thenumber of trains per group with the average passenger throughput pertrain, and is normalized against the local-train only service ofconventional two-track subway lines (1.0). This passenger throughputvaries from a high of 6.4, for longer train groups of four trains (threeof which are express trains) to a low of 0.25 for two-train groups withshort trains (0.10 times the length of the platform). These variationsin passenger throughput can be applied to variations in passenger demandover each day, week, and year.

In the examples considered in connection with Table 2 and as describedabove, a standard local-only headway is five minutes. To increase thethroughput on such a local-only subway line with five minute headway bya factor of six, one must dispatch six local trains every five minutes.which amounts to a headway of about 0.833 minutes. In contrast,operation of a four-train group according to either of the physical orvirtual passing techniques, this same throughput gain of 6.4 can beattained with a headway of 1.25 minutes, which is dramatically safer tooperate. Of course, as mentioned above, the safety of such a system canbe further increased by use of collision avoidance systems,electromagnetic braking, and other modern techniques.

Typically, most conventional existing local-only subway lines commonlyoperate with a standard dispatching interval of five to six minutes ofheadway, over the one-third of the working day deemed to be “rush hour”,at which peak passenger demand occurs. As mentioned above, to attain thefactor-of-six throughput gain during such peak times, a local-onlysubway line must dispatch six times the number of trains (assuming theshortened headway is tolerable). In contrast, according to embodimentsof this invention, this same throughput can be attained with fewerphysical trains.

In addition, this throughput increase is also useful in off-peak times.Conventional train lines avoid unprofitable under-loading by reducingthe frequency of service during off-peak times. Unfortunately, this hasthe effect of dramatically increasing passenger wait times at thestations, which makes subway travel less convenient and which thus oftenresults in further reduction in passenger demand (and, conceivably, evenfurther reductions in train frequency to compensate). In contrast,according to embodiments of the invention using the shorter trains, assummarized in the bottom-most rows of Table 2. As evident from thoseentries in Table 2, a group train with two shortened trains caneffectively replace a single local-only train, while still providingnearly 50% reduction in passenger travel time. Indeed, it iscontemplated that such short trains can be operated during most of theday on a vast majority of the two-track subway lines currently in use inthe world, providing the advantages of reduced operating cost andreduced passenger travel time, while maintaining the same frequency ofservice as provided during peak times.

To efficiently manage these shortened train times, and indeed variationsin train length over the day/week/year according to optimizationdeterminations made by system 20 in light of passenger demand, it willbe useful to implement modern coupling technologies in the trains, forexample as currently in use in many airport trains and trams. Additionalsafety and operational technologies such as closed-circuit televisionmonitoring and automated door opening and closing can provide furtherimprovements in the overall flexibility and efficiency of operating asubway line while optimizing train length relative to passenger demand,in this manner.

It is further contemplated that modern and future transportationtechnologies such as collision avoidance systems and the like can beused to reduce train travel times, and thus passenger travel times. Forexample, the implementation of collision avoidance systems in the frontand rear of each train can enable nearly bumper-to-bumper operation ofsubway line SLINE, as simultaneous or otherwise coordinated brakingtimes can be enforced. Additional technologies such as electromagnetictrack brakes and the like can also improve these train travel times byreducing braking times and distances.

Dynamic Synchronized Express and Local Train Scheduling

Considering the foregoing description, in a general sense, it iscontemplated that the particular expressions and their evaluation, foroptimization of such parameters as passenger travel time, throughput,infrastructure and rolling stock efficiency, and the like, can bereadily derived and evaluated by system 20 for a given set ofconstraints or choices in the number and arrangement of stations,trains, and other infrastructure. It is also contemplated thatstatistical analysis of these parameters and their optimization based onpassenger demand generally, passenger demand by time of day and day ofthe week, passenger demand by origin and destination station, and thelike, can be incorporated into the optimization performed by system 20in deriving, managing, and adjusting the subway schedule. It is alsocontemplated that those skilled in the art having reference to thisspecification will be readily able to carry out such optimization ofpassenger travel time, or optimization of other parameters important tothe subway operator or its customers, without undue experimentation.

As mentioned above in connection with the Background of the Invention,the passenger load during non-rush hour periods of the workday, as wellas during weekends and holidays, is much lower than during rush hourperiods. In addition, the subway system is operating in a non-rush hourperiod over a large majority of the time. According to anotherembodiment of this invention, separate optimizations of the operation ofone or more subway lines, for rush hour and non-rush periods, can beperformed by system 20, according to another embodiment of thisinvention. According to another aspect of this invention, the efficiencyand utilization of infrastructure, rolling stock, personnel, and otherresources during non-rush hour periods of the day can be optimized. Inaddition, these embodiments of the invention, and variations thereof,perform non-rush hour optimization and scheduling that improves theutilization of the subway system resources during non-rush houroperation, without significantly impacting the frequency of serviceprovided to the traveling public.

Referring now to FIG. 17 a, in comparison with FIG. 3 c, the separateoptimization and distinct operation of subway line SLINE in non-rushhour periods relative to such operation during rush hour will now bedescribed. For example, the operation of express trains EXP1, EXP2, etc.and local trains LOC0, LOC1, etc. during a rush-hour period cancorrespond to that shown in FIG. 3 c and described in detail above. Ateach express station E1 through E6, an express train EXPx passes apreviously-arrived local train LOCy, such passing either being performedphysically (i.e., the express train EXPx physically passes local trainLOCy) or “virtually” (i.e., the local train LOCy becomes an expresstrain over the next express interval, and vice versa). Considering agroup train to consist of the group of trains meeting at an expressstation (with the express train physically or virtually passing thelocal trains in its group), the group train dispatching interval refersto the time interval between successive group train departure times froma given express station. As described above, this group traindispatching interval (“GTDI”) is essentially constant over subway lineSLINE. In the example of FIG. 3 c, the GTDI corresponds to the timeinterval between successive points t1, t2, t3, t4, etc.

According to this embodiment of the invention, the GTDI is scaled to belonger in non-rush hour periods than during rush hour periods. FIG. 17 aillustrates the operation of subway line SLINE in a non-rush hour periodin which the GTDI is scaled by a factor of two. In the example of FIG.17 a, group trains depart express station E0 at times t2, t4, t6, t8;those points thus define a GTDI that is twice that of the rush-hour caseof FIG. 3 c. By doubling the GTDI, as shown in FIG. 17 a, the number ofexpress stations is reduced by a factor of two, because the longer GTDIresults in a longer time before an express train in one group catchesthe local train in the previously-dispatched group. The express stationinterval (in distance) between express stations is thus effectivelydoubled, assuming a constant travel velocity for express trains EXPx(and local trains LOCy) along the line. As such, express train EXP1leaving express station E0 at time t2 does not meet local train LOC0from the previously-dispatched group until time t4, at express stationE2 (pass point 2P10). Express train EXP2 does not catch up to localtrain LOC0 from two groups prior until time t6, at express station E3(pass point 4P20). In the diagram of FIG. 17 a, the only expressstations remaining are express stations E0, E2, E4, E6; express stationsE1, E3, E5 (which operate as express stations during rush-hour, as shownin FIG. 3 c) are not operating as express stations during this non-rushhour period.

FIG. 17 b illustrates the operation of subway line SLINE in a non-rushhour period in which the GTDI is scaled by a factor of three from thatused during rush hour (FIG. 3 c). In this example, group trains aredispatched from express station E0 at times t3, t6, t9, etc., whichtriples the time interval between passing points along line SLINE. Thistripled GTDI effectively triples the express station interval (indistance) between express stations at which passing occurs. In thisexample, express train EXP1 leaving express station E0 at time t3 doesnot meet local train LOC0 from the previously-dispatched group untiltime t6, which occurs at express station E3 (pass point 3P10).Similarly, express train EXP2 does not catch up to local train LOC0 fromtwo groups prior until time t12, at express station E6 (pass point6P20). In this tripled GTDI case, express stations E0, E3, E6, E9continue to operate as express stations, while express stations E1, E2,E4, E5, E7, E8 do not.

According to the examples of FIGS. 17 a and 17 b, the scaled or extendedGTDI and express station interval operation provides importantadvantages in the operation of a subway line. A foremost advantage isthat express service continues to be provided to the subway passengers,even during non-rush hour periods, in much the same manner as describedabove during rush hour periods. Many passengers can thus take advantageof greatly reduced subway travel time, even during these non-rush hourperiods; it is contemplated that ridership and profitability canincrease over the entire day (and year) as a result. Furthermore, it isapparent from FIGS. 17 a and 17 b that the number of trains running onsubway line SLINE during non-rush hour periods is greatly reducedrelative to that during rush hour periods. This is, of course,consistent with the much lower level of passenger demand during non-rushhour periods. As a result, express train service can be provided incombination with local service during these non-rush hour periods, whilestill attaining a high level of train and personnel utilization. Theoperational economy of the subway line during non-rush hours is thusimproved in much the same manner as during rush-hour periods.

From the viewpoint of the subway passengers, it is of course desirableto maintain a similar frequency of service during non-rush hour periodsas during rush hours. If the number of trains is simply reduced byscaling the GTDI, and if those trains have the same velocity as in therush hour period, however, the frequency of service will necessarilydecrease. According to this embodiment of the invention, however, goodfrequency of service is maintained during non-rush hour periods, evenwith the scaled GTDI operation described above, through the use ofsemi-express stations similarly as described above relative to FIGS. 9 band 9 c. As described above, those semi-express stations can be servedby express trains EXPx over the express station interval, by using thetime that those express trains EXPx would otherwise be waiting at anexpress station (i.e., queued behind the previously-arriving localtrains).

According to another embodiment of the invention, which will bedescribed in connection with FIG. 17 c, additional time is provided forexpress trains EXPx to make additional semi-express stops over the firstscaled express interval by advancing their departure time from the firstexpress station. Similarly, additional semi-express stops can beprovided over the last scaled express interval by delaying the arrivaltime of express trains EXPx at the final express. According to thisembodiment of the invention, the arrival and departure times at expressstations serving the scaled express intervals between the first and lastscaled express intervals are not altered, thus maintaining the passingoperations at intermediate express stations in the manner describedabove.

FIG. 17 c illustrates an example of this advanced and delayed expresstrain operation. In this example, the GTDI is scaled by a factor of twofrom its rush-hour time, and as such the number of express stations isreduced by a factor of two (similarly as described above relative toFIG. 17 a). However, the departures of express trains EXPx from initialexpress station E0 are advanced by a time Ta; in addition, the arrivalof express trains EXPx at terminal express station E6 are delayed by atime Td. This delay is illustrated in FIG. 17 c for the case of expresstrain EXP2D. Rather than departing express station E0 at time t4(shortly before the departure of local train LOC2), express train EXP2Ddeparts express station E0 at an earlier time (t4−Ta). This allows timefor express train EXP2D to make additional semi-express stops along theinterval between express stations E0 and E2, yet still catch up to localtrain LOC1 at express station E1 at time t6. Express train EXP2D travelsat its usual express velocity over the interval between express stationsE2 and E4, including such semi-express stops over that interval asallowed by the queuing time at express station E4 as described above.Over the final express interval between express stations E4 and E6,however, the average express velocity of express train EXP2D is reducedby making additional semi-express stops over that interval. As a result,the arrival time of express strain EXP2D at express station E6 isdelayed by a time Td from time t10 (at which time non-delayed expresstrain EXP2 would have arrived).

The number of additional semi-express stops made over the first and lastexpress intervals, and thus the advance departure time Ta and thedelayed arrival time Td, of course depends on the time Tse required formaking a semi-express stop. Shorter semi-express stop times Tse will, ofcourse, increase the number of stops that can be made for given valuesTa, Td.

Those skilled in the art having reference to this specification willcomprehend, from the example approaches illustrated in FIGS. 17 athrough 17 c and described above, that the number of non-rush hourexpress intervals relative to the rush hour express intervals (i.e., thescaling factor applied to the GTDI) can vary. At an extreme, a singlenon-rush hour express interval can be used, with the departure orarrival of the express train advanced or delayed in the manner shown inFIG. 17 c. A less extreme case can use two express intervals, with anexpress train making a single pass (virtual or physical) at anintermediate station; the advanced departure and delayed arrivalapproach of FIG. 17 c can be used in this two interval case, ifadditional semi-express stops are desired.

In any case, the scaling of the GTDI for non-rush hour time periods,relative to that during rush hours, will necessarily compromise thefrequency of train service along the subway line, involving a tradeoffbetween the economics of the subway system (favoring greater reductionin frequency of train service) and passenger convenience (favoringlesser reduction in frequency of train service). The optimum value ofthis scaling factor and the resulting operation is contemplated to beinstallation-dependent; more specifically, the optimization of thedynamic synchronized local and express train scheduling according toembodiments of this invention is contemplated to depend on the length ofthe subway line, the number of potential semi-express stationinstallations, whether the advanced departure time Td and delayedarrival time Ta can be utilized (and if so, the values for times Td,Ta), and on other operational methods and constraints. It iscontemplated that those skilled in the art having reference to thisspecification will be readily able to optimize the implementation ofthese embodiments of the invention for their specific implementationsand customer demand.

Various integer scaling factors as applied to an example of subway lineSLINE are illustrated in FIG. 17 d. In this example, the baseline rushhour implementation of subway line SLINE has twelve express stationintervals between thirteen express stations E0 through E12. For purposesof this example, four local stations (not shown in FIG. 17 d) aredisposed within each express station interval, such that the entire lineSLINE includes sixty local stations, plus the origin station E0. Alsofor purposes of this example, the local train travel time along thissubway line SLINE from origin to terminus is 120 minutes, and theexpress train travel time is half that, at 60 minutes. FIG. 17 dillustrates the location of express stations that result from scalingfactors E=1 (i.e., no change from rush hour), E=2, E=3, E=4, and E=6.

The performance results of subway line SLINE for these various scalingfactors E are tabulated in Table 3:

TABLE 3 Local/express # of express Number of trains Train # of local andone-way intervals Non-rush on track (one Equivalent utilization expressstations travel times Scaling (non-rush hour GTDI way-local + headwayefficiency (rush hour) (minutes) factor E hour) (minutes) express)(minutes) (normalized) 60 local; Local: 120; 1 12 5 36 2.5 0.16 12express express: 60 (24 local + (plus origin) 12 express) 2 6 10 18 5.00.33 (12 + 6) 3 4 15 12 7.5 0.50  (8 + 4) 4 3 20  9 10.0 0.66  (6 + 3) 62 30  6 15.0 1.0  (4 + 2)The results of Table 3 are shown for the example in which the GTDI oftrains departing origin express station E0 is five minutes (i.e., thetime Δt between times t1 and t0 of FIG. 3 d is five minutes). Asdescribed above, three trains (or group trains, when applicable) arepresent on every express interval: these three trains include theexpress train, the local train that left immediately after the expressstation at the origin end of the express station interval, and the localtrain that the express train will catch up to at the destination end ofthe express station interval. As such, for the rush hour case,thirty-six trains (twelve intervals with three trains each) are on trackat any given time along subway line SLINE. The equivalent average trainheadway is 2.5 minutes in this case, since two trains are dispatched atthe origin every five minutes.

As described above, the scaling factor lengthens the express stationinterval (and thus the GTDI), and thus reduces the number of expressstation intervals from the rush hour value. As shown in Table 3, scalingfactor E=6 lengthens the GTDI by a factor of six, from five minutes tothirty minutes, and reduces the number of express intervals by a factorof six, from twelve to two. As evident from Table 3, the higher scalingfactor reduces the number of trains on track at any given time; forscaling factor E=6, one-sixth the number of trains are on track duringnon-rush hour periods than during rush hour. Conversely, the trainutilization efficiency with scaling factor E=1 is 0.16 times (i.e.,one-sixth of) that of the non-rush hour period with scaling factor E=6.

As evident by a comparison of Table 3 for the various scaling factors E,one can evaluate the tradeoff between subway line economics and customerconvenience. For example, considering that operating cost is reduced byreducing the number of trains on track, the best train utilizationefficiency is that provided by the case of the highest possible scalingfactor value (which is E=6 in this example). Conversely, customerconvenience is improved by more frequency train service, or lowerequivalent headway times; this is provided by scaling factor E=1. Thescaling factors E=2, E=3, and E=4 in Table 3 and FIG. 17 d thusillustrate middle ground situations between the extreme scaling factorsE=1 and E=6, any one of which may be optimal for a particular subwayline and passenger population. It is contemplated that those skilled inthe art having reference to this specification will be readily able toevaluate such tradeoffs, for each subway line of interest. In addition,it is also contemplated that those skilled in the art having referenceto this specification will be able to similarly compare the operation ofthe rush hour and non-rush hour alternatives relative to a conventionalsubway system in which only local trains are dispatched.

In any case, it is contemplated that the length of each of the local andexpress trains utilized in the non-rush hour time periods can beadjusted to match the relative passenger demand. Shorter trains (or, asdescribed above relative to FIGS. 7 a through 7 c, fewer trains pergroup) can be used during those times of day, and days of the week oryear, at which passenger demand is lower than during rush hour. Thisreduction in train length will, of course, also improve the economicperformance of the subway line throughout the day, week, and year.

The alternative implementations shown in FIGS. 17 a through 17 d for thenon-rush hour implementation are applicable to either physical orvirtual passing occurring at express stations. However, it iscontemplated that either of these passing operations will necessarilyinvolve some amount of extra time at the express station, for one orboth of the trains involved. It has been observed that this additionaltime, if properly considered, tends to favor the use of semi-expressstations over express stations, because the passing time is not requiredfor stops at semi-express stations.

It has been discovered, through theoretical analysis of variousalternatives, that the use of two elongated express station intervals,with a relatively large number of semi-express stations deployed alongeach of the two express station intervals, can provide optimum trainutilization efficiency with acceptable equivalent headway times. Anexample of this situation is shown in FIG. 17 d by the line for scalingfactor E=6, in which the only express stations are origin station E0,express station E6, and terminus station E12 (for eastbound traffic).This is because the number of trains on track within each expressstation interval remains at three trains, for each direction; fortwo-way service on a dual express station interval implementation,twelve trains total are on track at any given time. The actualequivalent headway experienced by passengers, relative to conventionallocal-only service (as is typically implemented during non-rush hourperiods), will depend on the length of the overall subway line. For verylong subway lines (e.g., beyond a sixty-station subway line with twohour one-way local travel time from end to end), in order to keep theequivalent headway within acceptable bounds, the use of three elongatedexpress station intervals may become necessary, at a cost of increasingthe number of trains on track to nine trains in each direction. Anexample of this situation is shown in FIG. 17 d by the line for scalingfactor E=4, in which express stations E0, E4, E8, and E12 are in use. Ineither case, semi-express stations will be utilized by the expresstrains over these elongated express station intervals.

As shown in the generalized flow diagram of FIG. 3 b, and as mentionedabove, optional process 39 for generating a non-rush hour schedule anddeployment of express and subway trains can be executed by system 20(FIG. 3 a), according to this embodiment of the invention, consideringthe alternative implementations including the various scaling factors asdescribed above. This non-rush hour schedule is contemplated to be inaddition to the rush hour schedule described above in connection withprocesses 34, 36, 38 described above. As in the case of the rush hourschedule, the optimizations involved in generating this non-rush hourschedule are based on various sources of data and information, includingpassenger data source 33, train data source 35, and station data sourcd37, all of which are stored in library 32 and which contain informationsuch as that described above in connection with FIG. 3 b. Other dataregarding other parameters useful to the scheduling process, areaccessed or otherwise available to system 20 in carrying out thescheduling of this non-rush hour schedule.

It is contemplated that this non-rush hour scheduling process 39 can becarried out by way of various algorithmic approaches, for example asexecuted by computational resources within system 20 executing programinstructions in an automated or “artificial intelligence” manner. In ageneral sense, process 39 contemplates the execution of programinstructions by computational resources within system 20 to define thescaling factor best suited for the particular construction of subwayline, passenger demand, and operational cost and availability of trainsto subway line SLINE. For example, these computational resources mayevaluate a cost function that expresses criteria involved in definingthe numbers, lengths, and arrangement of express intervals, trains ontrack, length of the trains, and location of express and semi-expressstations to be used in these non-rush hour periods. As described above,parameters representative of passenger throughput, passenger traveltime, passenger comfort (i.e., avoiding overcrowded conditions), andsubway train utilization, may be reflected in the cost function that isoptimized in scheduling process 39. It is contemplated that thoseskilled in the art having reference to this specification will be ableto apply conventional AI and other evaluation techniques to define thenumber and frequency of express trains for the current informationrelative to subway line SLINE, in this process 39.

As described above in connection with process 38, computationalresources within system 20 operate within process 39 to derive aschedule for subway line SLINE during this non-rush hour period, inwhich the operation of express and local trains are synchronized so thatexpress and local trains meet in time only at those stations defined asexpress stations. As described above, these express stations will allowfor express trains to pass the slower-traveling local trains, eitherphysically or virtually. This derivation in process 39 is contemplatedto be, in many cases, an iterative process by way of which certainvariables are adjusted or incremented to identify an optimum combinationgiven the economic, passenger-driven, and management-specifiedconstraints on subway line SLINE. As described above, the scheduledeveloped by process 39 will be communicated to passengers in process40, and adjusted in response to real-time operational data 41 ifdesired, in process 42.

IN CONCLUSION

The embodiments of this invention described in this specificationprovide tremendous advantages in the construction and operation ofsubway train lines, particularly in urban areas for serving commutersand other passengers. These embodiments of this invention enableoptimization of the operation of a two-track subway line, to provideimproved passenger travel times and improved passenger throughputwithout requiring massive infrastructure costs, such as undue excavationand underground construction in building or rebuilding subway stations,or the construction costs of separate express rail lines. As a result,it is contemplated that the subway overcrowding now being experienced inmany cities in the world can be reduced, at minimal additional expense.In addition, it is contemplated that these embodiments of the inventionwill provide great flexibility to the subway operator in scheduling andoperating the subway lines, and flexible and beneficial options to manypassengers in improving their travel experience. Furthermore, it iscontemplated that feedback control and adjustment of the operation ofthe subway system will be enabled by application of these optimizationtechniques. In addition, embodiments of this invention enable thesynchronized connections between express and local trains to beoptimized differently in non-rush-hour periods than during rush hourperiods, which allows the system operator to fully optimize operation ofcommuter rail systems at all times of the day and all days of the week,and throughout the year.

While this invention has been described according to its embodiments, itis of course contemplated that modifications of, and alternatives to,these embodiments, such modifications and alternatives obtaining theadvantages and benefits of this invention, will be apparent to those ofordinary skill in the art having reference to this specification and itsdrawings. It is contemplated that such modifications and alternativesare within the scope of this invention as subsequently claimed herein.

1-6. (canceled)
 7. A method of operating a subway line having a singletrack in a direction of travel, comprising the steps of: operating alocal train to travel along the track from a first express stationtoward a second express station; operating an express train to travelalong the single track behind the local train, the express train leavingthe first express station later than the local train but traveling at afaster travel velocity to arrive at the second express station at ornear the time that the local train is at the second express station; andpassing the local train with the express train at the second expressstation; wherein the second express station includes a passengerplatform; wherein the step of operating the local train comprises:operating a first train to travel along the single track from the firstexpress station, stopping for passenger transfer at least one time at alocal station along the subway line between the first and second expressstations; wherein the step of operating the express train comprises:operating a second train to travel along the single track withoutstopping at the local station, the second train leaving the firstexpress station later than the first train but traveling at a fastertravel velocity; wherein the passing step comprises: stopping the firsttrain at the second express station to allow passengers to board andde-board the first train from and to the passenger platform; thenoperating the first train to proceed along the single track from thesecond express station as an express train; then stopping the secondtrain at the second express station to allow passengers to board andde-board the second train from and to the passenger platform; and thenoperating the second train to proceed along the single track from thesecond express station as a local train, the second train stopping forpassenger transfer at least one time at a local station along the subwayline after the second express station; and wherein the step of operatingthe first train as an express train comprises operating the first trainto travel without stopping at the local station after the second expressstation.
 8. The method of claim 7, wherein the step of operating theexpress train further comprises: operating a third train to travel alongthe single track without stopping at the local station, the third trainleaving the first express station later than the first train buttraveling at a faster travel velocity, and leaving the first expressstation earlier than the second train; and and wherein the passing stepfurther comprises: after the step of operating the first train toproceed along the single track from the second express station as anexpress train, and before the step of stopping the second train at thesecond express station: stopping the third train at the second expressstation to allow passengers to board and de-board the third train fromand to the passenger platform; and then operating the third train toproceed along the single track from the second express station as anexpress train.
 9. The method of claim 8, wherein the step of operatingthe express train further comprises: stopping the third train along thesingle track between the first and second express stations at a localstation at which the second train does not stop but at which the firsttrain stops.
 10. The method of claim 8, further comprising: operating afourth train to travel along the single track without stopping at thelocal station, the fourth train leaving the first express station laterthan the first train but traveling at a faster travel velocity, andleaving the first express station earlier than the second train; andafter the step of operating the first train to proceed along the singletrack from the second express station as an express train, and beforethe step of stopping the second train at the second express station:stopping the fourth train at the second express station to allowpassengers to board and de-board the fourth train from and to thepassenger platform; and then operating the fourth train to proceed alongthe single track from the second express station as an express train.11. The method of claim 7, wherein the step of stopping the second trainat the express station occurs after only a brief time after the step ofoperating the first train to proceed along the single track from thesecond express station begins.
 12. The method of claim 7, furthercomprising: before the step of stopping the first train at the secondexpress station to allow passengers to board and de-board the firsttrain from and to the passenger platform, stopping the first train atthe second express station so that at least a portion of the passengerplatform is not aligned with the passenger platform; then stopping thesecond train at the second express station so that a front portion ofthe first train aligns with a portion of the passenger platform at thesecond express station, to allow passengers to de-board the second trainto the passenger platform; wherein the step of stopping the first trainat the second express station to allow passengers to board and de-boardthe first train from and to the passenger platform is performed afterpassengers have de-boarded the second train to the passenger platform;and further comprising: then stopping the second train at the secondexpress station to allow passengers to board and de-board the secondtrain from and to the passenger platform.
 13. The method of claim 7,wherein the step of operating the express train further comprises:operating a third train to travel along the single track withoutstopping at the local station, the third train leaving the first expressstation later than the first train but traveling at a faster travelvelocity, and leaving the first express station earlier than the secondtrain; before the step of stopping the first train at the second expressstation to allow passengers to board and de-board the first train fromand to the passenger platform, stopping the second and third trains atthe second express station so that a front portion of the third trainaligns with a portion of the passenger platform at the second expressstation, to allow passengers to de-board the third train to thepassenger platform; wherein the step of stopping the first train at thesecond express station to allow passengers to board and de-board thefirst train from and to the passenger platform is performed afterpassengers have de-boarded the third train to the passenger platform;and further comprising: then stopping the third train at the secondexpress station to allow passengers to board and de-board the thirdtrain from and to the passenger platform.
 14. The method of claim 7,further comprising: operating a third train to travel along the singletrack without stopping at the local station, the third train leaving thefirst express station later than the first train but traveling at afaster travel velocity, and leaving the first express station earlierthan the second train; operating a fourth train to travel along thesingle track without stopping at the local station, the fourth trainleaving the first express station later than the first train buttraveling at a faster travel velocity, and leaving the first expressstation earlier than the second train; before the step of stopping thefirst train at the second express station to allow passengers to boardand de-board the first train from and to the passenger platform,stopping the third and fourth trains at the second express station sothat a front portion of the fourth train aligns with a portion of thepassenger platform at the second express station, to allow passengers tode-board the fourth train to the passenger platform; wherein the step ofstopping the first train at the second express station to allowpassengers to board and de-board the first train from and to thepassenger platform is performed after passengers have de-boarded thefourth train to the passenger platform; and further comprising: thenstopping the fourth train at the second express station to allowpassengers to board and de-board the fourth train from and to thepassenger platform.
 15. (canceled)
 16. A method of operating a computersystem to manage the scheduling and operating of a subway line having asingle track in a direction of travel, comprising the steps of:retrieving, from a memory resource, data representative of passengerusage of the subway line; retrieving, from a memory resource, datarepresentative of train resources and properties associated with thesubway line; retrieving, from a memory resource, data representative ofthe locations and properties of stations along the subway line; from theretrieved data, deriving a schedule of local and express trainsoperating along the subway line, relative to local and express stationsalong the subway line, in at least one direction of travel, so thattrains operating as express trains catch up to local trains leading theexpress trains along the subway line only at express stations; whereinthe derived schedule is based on express trains passing local trains atthe express stations; and wherein the data representative of propertiesof stations along the subway line comprises data representative of whichstations are express stations and which stations are local stations.17-19. (canceled)
 20. A method of operating a computer system to managethe scheduling and operating of a subway line having a single track in adirection of travel, comprising the steps of: retrieving, from a memoryresource, data representative of passenger usage of the subway line;retrieving, from a memory resource, data representative of trainresources and properties associated with the subway line; retrieving,from a memory resource, data representative of the locations andproperties of stations along the subway line; from the retrieved data,deriving a schedule of local and express trains operating along thesubway line, relative to local and express stations along the subwayline, in at least one direction of travel, so that trains operating asexpress trains catch up to local trains leading the express trains alongthe subway line only at express stations; wherein the derived scheduleis based on express trains passing local trains at the express stations;and wherein the step of deriving the schedule comprises: also derivingcar assignments corresponding to time of day and to origin anddestination stations for a passenger trip.
 21. The method of claim 20,further comprising: communicating the derived schedule and carassignments to passengers.
 22. The method of claim 21, wherein thecommunicating step is performed by way of one or more of a groupconsisting of video displays at stations, video displays on trains, andinformation communicated along with purchased tickets.
 23. The method ofclaim 21, wherein the derived schedule and car assignments communicatedto passengers also comprises: identification of stations at which apassenger may transfer forward to a train ahead of the train thepassenger is currently riding on.
 24. A method of operating a computersystem to manage the scheduling and operating of a subway line having asingle track in a direction of travel, comprising the steps of:retrieving, from a memory resource, data representative of passengerusage of the subway line; retrieving, from a memory resource, datarepresentative of train resources and properties associated with thesubway line; retrieving, from a memory resource, data representative ofthe locations and properties of stations along the subway line; from theretrieved data, deriving a schedule of local and express trainsoperating along the subway line, relative to local and express stationsalong the subway line, in at least one direction of travel, so thattrains operating as express trains catch up to local trains leading theexpress trains along the subway line only at express stations; whereinthe derived schedule is based on express trains passing local trains atthe express stations; wherein the deriving step derives a rush-hourschedule, in which a first plurality of stations along the subway lineare identified as express stations; and further comprising: from theretrieved data, deriving a non-rush hour schedule of local and expresstrains operating along the subway line, relative to local and expressstations along the subway line, in at least one direction of travel, sothat trains operating as express trains catch up to local trains leadingthe express trains along the subway line only at express stations;wherein the derived schedule is based on express trains passing localtrains at the express stations; and wherein the step of deriving thenon-rush hour schedule identifies a second plurality of stations alongthe subway line as express stations, the second plurality of stationsbeing a subset of the first plurality of stations.
 25. (canceled)
 26. Acomputer-readable medium storing a computer program that, when executedon a computer system, causes the computer system to perform apluralitperations for manain the scheduling and operation of a subwayhaving a single track in a direction of travel, the plurality ofoperations comprising: retrieving, from a memory resource in thecomputer system, data representative of passenger usage of the subwayline; retrieving, from a memory resource in the computer system, datarepresentative of train resources and properties associated with thesubway line; retrieving, from a memory resource in the computer system,data representative of the locations and properties of stations alongthe subway line; from the retrieved data, deriving a schedule of localand express trains operating along the subway line, relative to localand express stations along the subway line, in at least one direction oftravel, so that trains operating as express trains catch up to localtrains leading the express trains along the subway line only at expressstations; wherein the derived schedule is based on express trainspassing local trains at the express stations; and wherein the datarepresentative of properties of stations along the subway line comprisesdata representative of which stations are express stations and whichstations are local stations. 27-29. (canceled)
 30. A computer-readablemedium storing a computer program that, when executed on a computersystem, causes the computer system to perform a plurality of operationsfor managing the scheduling and operation of a subway line having asingle track in a direction of travel, the plurality of operationscomprising: retrieving, from a memory resource in the computer system,data representative of passenger usage of the subway line; retrieving,from a memory resource in the computer system, data representative oftrain resources and properties associated with the subway line;retrieving, from a memory resource in the computer system, datarepresentative of the locations and properties of stations along thesubway line; from the retrieved data, deriving a schedule of local andexpress trains operating along the subway line, relative to local andexpress stations along the subway line, in at least one direction oftravel, so that trains operating as express trains catch up to localtrains leading the express trains along the subway line only at expressstations; wherein the derived schedule is based on express trainspassing local trains at the express stations; and wherein the operationof deriving the schedule comprises: also deriving car assignmentscorresponding to time of day and to origin and destination stations fora passenger trip.
 31. The computer-readable medium of claim 30, whereinthe plurality of operations further comprises: communicating the derivedschedule and car assignments to passengers.
 32. The computer-readablemedium of claim 31, wherein the communicating operation is performed byway of one or more of a group consisting of video displays at stations,video displays on trains, and information communicated along withpurchased tickets.
 33. The computer-readable medium of claim 31, whereinthe derived schedule and car assignments communicated to passengers alsocomprises: identification of stations at which a passenger may transferforward to a train ahead of the train the passenger is currently ridingon.
 34. A computer-readable medium storing a computer program that, whenexecuted on a computer system, causes the computers system to perform aplurality operations for managing the scheduling and operation of asubway line having a single track in a direction of travel, theplurality of operations comprising: retrieving, from a memory resourcein the computer system, data representative of passenger usage of thesubway line; retrieving, from a memory resource in the computer system,data representative of train resources and properties associated withthe subway line; retrieving, from a memory resource in the computersystem, data representative of the locations and properties of stationsalong the subway line; from the retrieved data, deriving a schedule oflocal and express trains operating along the subway line, relative tolocal and express stations along the subway line, in at least onedirection of travel, so that trains operating as express trains catch upto local trains leading the express trains along the subway line only atexpress stations; wherein the derived schedule is based on expresstrains passing local trains at the express stations; wherein thederiving operation derives a rush-hour schedule, in which a firstplurality of stations along the subway line are identified as expressstations; and wherein the plurality of operations further comprises:from the retrieved data, deriving a non-rush hour schedule of local andexpress trains operating along the subway line, relative to local andexpress stations along the subway line, in at least one direction oftravel, so that trains operating as express trains catch up to localtrains leading the express trains along the subway line only at expressstations; wherein the derived schedule is based on express trainspassing local trains at the express stations; and wherein the operationof deriving the non-rush hour schedule identifies a second plurality ofstations along the subway line as express stations, the second pluralityof stations being a subset of the first plurality of stations. 35.(canceled)
 36. A computer system for managing the scheduling andoperation of a subway line having a single track in a direction oftravel, comprising: an input device for receiving inputs from a user ofthe system; at least one memory resource for storing data, the dataincluding data representative of inputs from the user of the system; oneor more central processing units coupled to the input device, forexecuting program instructions; and program memory, coupled to the oneor more central processing units, for storing a computer programincluding program instructions that, when executed by the one or morecentral processing units, cause the computer system to perform aplurality of operations for managing the scheduling and operation of asubway line having a single track in a direction of travel, theplurality of operations comprising: retrieving, from a memory resource,data representative of passenger usage of the subway line; retrieving,from a memory resource, data representative of train resources andproperties associated with the subway line; retrieving, from a memoryresource, data representative of the locations and properties ofstations along the subway line; from the retrieved data, deriving aschedule of local and express trains operating along the subway line,relative to local and express stations along the subway line, in atleast one direction of travel, so that trains operating as expresstrains catch up to local trains leading the express trains along thesubway line only at express stations; wherein the derived schedule isbased on express trains passing local trains at the express stations;and wherein the data representative of properties of stations along thesubway line comprises data representative of which stations are expressstations and which stations are local stations. 37-39. (canceled)
 40. Acomputer system for managing the scheduling and operation of a subwayline having a single track in a direction of travel, comprising: aninput device for receiving inputs from a user of the system; at leastone memory resource for storing data, the data including datarepresentative of inputs from the user of the system; one or morecentral processing units coupled to the input device, for executingprogram instructions; and program memory, coupled to the one or morecentral processing units, for storing a computer program includingprogram instructions that, when executed by the one or more centralprocessing units, cause the computer system to perform a plurality ofoperations for the scheduling and operation of a subway line having asingle track in a direction of travel, the plurality of operationscomprising: retrieving, from a memory resource, data representative ofpassenger usage of the subway line; retrieving, from a memory resource,data representative of train resources and properties associated withthe subway line; retrieving, from a memory resource, data representativeof the locations and properties of stations along the subway line; fromthe retrieved data, deriving a schedule of local and express trainsoperating along the subway line, relative to local and express stationsalong the subway line, in at least one direction of travel, so thattrains operating as express trains catch up to local trains leading theexpress trains along the subway line only at express stations; whereinthe derived schedule is based on express trains passing local trains atthe express stations; wherein the operation of deriving the schedulecomprises: also deriving car assignments corresponding to time of dayand to origin and destination stations for a passenger trip.
 41. Thesystem of claim 40, wherein the plurality of operations furthercomprises: communicating the derived schedule and car assignments topassengers.
 42. The system of claim 41, further comprising: at least oneoutput device, coupled to the one or more central processing units,comprising one or more of a group consisting of video displays atstations, video displays on trains, and information communicated alongwith purchased tickets; wherein the communicating operation is performedby way of the at least one output device.
 43. The system of claim 41,wherein the derived schedule and car assignments communicated topassengers also comprises: identification of stations at which apassenger may transfer forward to a train ahead of the train thepassenger is currently riding on.
 44. A computer system for managing thescheduling and operation of a subway line having a single track in adirection of travel, comprising: an input device for receiving inputsfrom a user of the system; at least one memory resource for storingdata, the data including data representative of inputs from the user ofthe system; one or more central processing units coupled to the inputdevice, for executing program instructions; and program memory, coupledto the one or more central processing units, for storing a computerprogram including program instructions that, when executed by the one ormore central processing units, cause the computer system to perform aplurality of operations for managing the scheduling and operation of asubway line having a single track in a direction of travel, theplurality of operations comprising: retrieving, from a memory resource,data representative of passenger usage of the subway line; retrieving,from a memory resource, data representative of train resources andproperties associated with the subway line; retrieving, from a memoryresource, data representative of the locations and properties ofstations along the subway line; from the retrieved data, deriving aschedule of local and express trains operating along the subway line,relative to local and express stations along the subway line, in atleast one direction of travel, so that trains operating as expresstrains catch up to local trains leading the express trains along thesubway line only at express stations; wherein the derived schedule isbased on express trains passing local trains at the express stations;wherein the deriving operation derives a rush-hour schedule, in which afirst plurality of stations along the subway line are identified asexpress stations; and wherein the plurality of operations furthercomprises: from the retrieved data, deriving a non-rush hour schedule oflocal and express trains operating along the subway line, relative tolocal and express stations along the subway line, in at least onedirection of travel, so that trains operating as express trains catch upto local trains leading the express trains along the subway line only atexpress stations; wherein the derived schedule is based on expresstrains passing local trains at the express stations; and wherein theoperation of deriving the non-rush hour schedule identifies a secondplurality of stations along the subway line as express stations, thesecond plurality of stations being a subset of the first plurality ofstations.